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Yang, C. Lee, R. K. Kotlanka, J. Xie and S. P. Lim, J. Micromech. Microeng. 20, 065017 (2010)."}]},{"reference":{"texkey":"POZ","imprint":{"publisher":"Wiley"},"label":"51","publication_info":{"year":2005},"misc":["Engineering (John","and Sons,)"],"authors":[{"full_name":"Microwave, D.M. Pozar"}]},"raw_refs":[{"schema":"text","source":"arXiv","value":"51. D. M. Pozar Microwave Engineering (John Wiley and Sons, 2005)."}]},{"reference":{"texkey":"vdWMWG","label":"52","publication_info":{"journal_volume":"87","artid":"062105","year":2013,"journal_title":"Phys.Rev.A"},"misc":["E and G. Kurizki"],"authors":[{"full_name":"Shahmoon, E."}]},"raw_refs":[{"schema":"text","source":"arXiv","value":"52. E. Shahmoon E and G. Kurizki Phys. Rev. A 87, 062105 (2013)."}],"record":{"$ref":"https://inspirehep.net/api/literature/3008875"}},{"reference":{"texkey":"ORF","urls":[{"value":"http://www.ece.rutgers.edu/~orfanidi/ewa/"}],"label":"53","publication_info":{"year":2016},"misc":["Electromagnetic Waves and Antennas, www.ece.rutgers.edu/∼orfanidi/ewa/"],"authors":[{"full_name":"Orfanidis, S.J."}]},"raw_refs":[{"schema":"text","source":"arXiv","value":"53. S. J. Orfanidis, Electromagnetic Waves and Antennas, www.ece.rutgers.edu/∼orfanidi/ewa/ (2016)."}]},{"reference":{"texkey":"Thanks","label":"54","misc":["Acknowledgments. We acknowledge fruitful discussions with Itay Griniasty, Konrad Lehnert, Mohammad Hamidian and Homer Reid, and financial support from the MIT-Harvard Center for Ultracold Atoms, ERC and ISF. Author contributions: E.S. designed the research and performed the calculations, E. S. and U. L. discussed the results and wrote the manuscript. Competing interests: The authors declare that they have no competing interests. Data and materials availability: All data needed to evaluate the conclusions in the paper are present in the paper and/or the Supplementary Materials. Additional data related to this paper may be requested from the authors. 𝑦 (c) 𝐼𝑁 𝑅 𝐶 𝑖𝑋 𝐶 𝑍 (b) 𝐼𝑁 𝑅 𝑅 (a) 𝑉𝑁 𝑅 = 𝜃 (d) 𝑍"]},"raw_refs":[{"schema":"text","source":"arXiv","value":"54. Acknowledgments. We acknowledge fruitful discussions with Itay Griniasty, Konrad Lehnert, Mohammad Hamidian and Homer Reid, and financial support from the MIT-Harvard Center for Ultracold Atoms, ERC and ISF. Author contributions: E.S. designed the research and performed the calculations, E. S. and U. L. discussed the results and wrote the manuscript. Competing interests: The authors declare that they have no competing interests. Data and materials availability: All data needed to evaluate the conclusions in the paper are present in the paper and/or the Supplementary Materials. Additional data related to this paper may be requested from the authors. 𝑦 (c) 𝐼𝑁 𝑅 𝐶 𝑖𝑋 𝐶 𝑍 (b) 𝐼𝑁 𝑅 𝑅 (a) 𝑉𝑁 𝑅 = 𝜃 (d) 𝑍"}]}],"referenced_authors_bais":["G.Kurizki.1","R.N.Kleiman.2","D.S.Ether.1","Pasi.Lahteenmaki.1","D.S.Dean.2","F.Intravaia.2","U.Mohideen.1","C.M.Wilson.1","D.Polder.1","S.Reynaud.1","John.M.Martinis.1","A.Tkatchenko.1","M.Simoen.1","R.S.Decca.1","A.Lambrecht.1","J.D.Whittaker.2","I.Kravchenko.1","D.Li.15","G.Bimonte.1","J.Hassel.2","M.D.LaHaye.1","A.Pourkabirian.1","J.L.Garrett.1","D.Iannuzzi.1","A.Hanke.1","J.R.Johansson.1","B.Pontes.1","V.A.Aksyuk.1","G.R.de.S.Araujo.1","J.Koch.1","T.M.Yu.1","D.Somers.1","F.Chen.1","P.A.Maia.Neto.1","M.T.H.Reid.1","M.Ansmann.1","H.B.Chan.1","D.Bishop.1","G.Johnson.1","A.Blais.1","M.Kardar.1","A.P.McCauley.1","A.N.Cleland.1","E.Fischbach.1","J.M.Gambetta.1","M.Weides.1","R.J.Schoelkopf.1","E.Lucero.1","R.Podgornik.1","R.Golestanian.1","H.B.G.Casimir.1","A.D.OConnell.1","T.Duty.1","J.Wenner.1","G.L.Klimchitskaya.2","Tan.Lu.1","M.Lenander.1","N.B.Viana.1","D.E.Krause.1","R.B.Rodrigues.2","T.Donner.1","A.W.Rodriguez.1","L.P.Pitaevskii.1","F.Nori.1","L.B.Pires.1","R.O.Behunin.2","J.N.Munday.1","A.Houck.1","F.S.S.da.Rosa.1","R.W.Simmonds.1","David.Schuster.1","I.Mazets.1","P.RodriguezLopez.1","A.Naji.1","Y.J.Suh.1","D.D.Lopez.1","T.Emig.1","M.L.Roukes.1","S.G.Johnson.1","G.S.Paraoanu.1","L.M.Woods.1","V.M.Mostepanenko.1","J.W.Harlow.1","R.R.Horgan.1","S.Umrath.1","P.J.Hakonen.1","Y.Ayala.1","M.S.Allman.1","K.Cicak.1","V.A.Parsegian.1","E.Shahmoon.1","G.L.Ingold.1","P.M.Echternach.1","K.C.Schwab.1","D.Sank.1","K.W.Lehnert.1","S.Frases.1","Y.Bao.5","G.Johansson.4","M.Hofheinz.1","S.M.Girvin.1","J.Majer.1","Michel.H.Devoret.1","Jia.Heng.Zou.1","E.M.Lifshitz.1","I.E.Dzyaloshinskii.2","Z.Marcet.1","Steven.K.Lamoreaux.1","R.C.Bialczak.1","Y.S.Barash.2","Timothy.H.Boyer.1","H.M.Nussenzveig.1","J.Sarabadani.1","F.Capasso.1","J.D.Teufel.1","Anushree.Roy.2","D.L.Martinez.1","A.J.Sirois.1","P.Delsing.1","D.A.R.Dalvit.1","H.Nyquist.1","M.Neeley.1","Hao.Hao.Wang.1"],"figures":[{"filename":"fig1.png","material":"preprint","caption":"\\small{ Generalized potentials induced by electronic quantum fluctuations. (a) Quantum noise source: resistive circuit elements are modeled by a resistor $R$ in parallel with a current noise source $I_N$ with the spectrum of Eq.~(\\ref{IN}) (or equivalently, in series with a voltage $V_N=R I_N$). (b) Capacitor embedded in a general passive circuit represented by its impedance $Z=R+iX$. The zero-point-induced potential built on the capacitor, Eq. (\\ref{U}), gives rise to a generalized force $f=-\\partial U/\\partial\\xi$ on its internal degree of freedom $\\xi$. (c) Examples of electromechanical capacitors: for the parallel-plate capacitor with separation $\\xi=y$ \\cite{TEU,LEHN}, $f$ is a force normal to the plates, whereas for the variable capacitor with rotation angle $\\xi=\\theta$ \\cite{ROT}, $f$ is a torque. (d) Superconducting qubit (SCQ) capacitively coupled to a circuit $Z$ (bottom: specific example of an $RC$ circuit). The zero-point fluctuations from $Z$ induce shifts in the energy levels of the SCQ in analogy to the Lamb shift. }} fig1","label":"fig1","source":"arxiv","key":"c0103a26f0bc7ee7f40be03d0326c160","url":"https://inspirehep.net/files/c0103a26f0bc7ee7f40be03d0326c160"},{"filename":"fig2a.png","material":"preprint","caption":"\\small{ Potential energy inside a capacitor. (a) Four simple cases for the general circuit of Fig.~1b. (b) Potential energy $U$, Eq. (\\ref{U}). For case I, $U$ from Eq. (\\ref{U1}) is plotted in units of $U_0=\\hbar/(2\\pi R C_0)$ and as a function of $r=C_0/C$ (solid line). For a parallel-plate capacitor with plate separation $y\\propto r$, the resulting relative force between the plates is repulsive. Dashed and dotted lines: same as solid line, for cases II and III with $U_0=\\hbar R/L$ and $U_0=(\\hbar/2\\pi) R/L$, respectively, and $r=L/(C R^2)$, both yielding an attractive force for a plate capacitor. (c) Same as (b) for case IV with $U_0=\\hbar/(R C_0)$ and $r=C_0/C$. Depending on the parameter $a=\\sqrt{L/C_0}/R$, both attractive ($a=0.5$, solid line) and repulsive ($a=2$, dashed line) potentials are possible. }} fig2","label":"fig2","source":"arxiv","key":"44910d338f356b1e832d05b75a4362a5","url":"https://inspirehep.net/files/44910d338f356b1e832d05b75a4362a5"},{"filename":"fig2b.png","material":"preprint","caption":"\\small{ Potential energy inside a capacitor. (a) Four simple cases for the general circuit of Fig.~1b. (b) Potential energy $U$, Eq. (\\ref{U}). For case I, $U$ from Eq. (\\ref{U1}) is plotted in units of $U_0=\\hbar/(2\\pi R C_0)$ and as a function of $r=C_0/C$ (solid line). For a parallel-plate capacitor with plate separation $y\\propto r$, the resulting relative force between the plates is repulsive. Dashed and dotted lines: same as solid line, for cases II and III with $U_0=\\hbar R/L$ and $U_0=(\\hbar/2\\pi) R/L$, respectively, and $r=L/(C R^2)$, both yielding an attractive force for a plate capacitor. (c) Same as (b) for case IV with $U_0=\\hbar/(R C_0)$ and $r=C_0/C$. Depending on the parameter $a=\\sqrt{L/C_0}/R$, both attractive ($a=0.5$, solid line) and repulsive ($a=2$, dashed line) potentials are possible. }} fig2","label":"fig2","source":"arxiv","key":"df31a5cc6b5e1791059e28d6425b7250","url":"https://inspirehep.net/files/df31a5cc6b5e1791059e28d6425b7250"},{"filename":"fig3.png","material":"preprint","caption":"\\small{ Comparison between the electronic zero-point force (blue solid line) and the standard Casimir force (red dashed line) acting between the plates of a parallel-plate capacitor. The capacitor with a capacitance $C=A\\varepsilon_0/y$ is assumed to be connected in series to a resistor, $R=10\\mathrm{\\Omega}$, and an inductor, $L=0.1$nH (circuit II of Fig. 2a). The forces are plotted as a function of the plate separation $y$, and the plate diameter is taken to be: (a) $15\\mu$m, and (b) $200\\mu$m. Due to its long-range scaling, the electronic zero-point force can become much stronger [see case (b) and text]. }} fig3","label":"fig3","source":"arxiv","key":"e5a7971b4822b9f0580e61f0386fd470","url":"https://inspirehep.net/files/e5a7971b4822b9f0580e61f0386fd470"},{"filename":"fig4.png","material":"preprint","caption":"\\small{ The ability to measure fluctuation potentials as a function of parameters of the environment (circuit) presents an interesting possibility opened by circuits for fluctuation-induced phenomena. (a,b,c): The force between the capacitor plates in the circuits (I,II,III) from Fig. 2a is plotted as a function of circuit parameters. Circuit (I) exhibits repulsive relative forces whereas circuits (II) and (III) exhibit attractive forces. In the limits of small $R$ for $f_{\\mathrm{II}}$ and large $R$ for $f_{\\mathrm{III}}$, both forces become identical to that in the isolated $LC$ circuit. All three cases are plotted using the physical parameters of the parallel-plate electromechanical capacitor of Ref. \\cite{TEU}, whose displacement-measurement sensitivity of $\\sim 10^{-32}$m$^2$Hz$^{-1}$ is estimated to be sufficient to detect the sub fN forces we find (text). (d) Shift in the transition frequency of a superconducting transmon qubit with $\\sqrt{E_C/8E_J}=0.1$, $C_g/C_J=0.1$ and $\\omega_0=2\\pi\\times5$GHz. Shifts of the order of $0.1\\%$ of the original transition frequency are observed, much larger than the acquired level width. }} fig4","label":"fig4","source":"arxiv","key":"23d513efcd79fb64a1abb457a4411a1d","url":"https://inspirehep.net/files/23d513efcd79fb64a1abb457a4411a1d"}],"inspire_categories":[{"term":"Quantum Physics","source":"arxiv"}],"preprint_date":"2018-04-29","author_count":2,"first_author":{"affiliations_identifiers":[{"schema":"ROR","value":"https://ror.org/03vek6s52"}],"full_name":"Shahmoon, Ephraim","last_name":"Shahmoon","first_name":"Ephraim","recid":1974218},"public_notes":[{"source":"arXiv","value":"Published version has open access"}],"control_number":3041658,"earliest_date":"2018-04-29","document_type":["article"],"texkeys":["Shahmoon:2018kgf"],"abstracts":[{"source":"arXiv","value":"One of the most intriguing manifestations of quantum zero-point fluctuations are the van der Waals and Casimir forces, often associated with vacuum fluctuations of the electromagnetic field. Here we study generalized fluctuation potentials acting on internal degrees of freedom of components in electrical circuits. These electronic Casimir-like potentials are induced by the zero-point current fluctuations of any general conductive circuit. For realistic examples of an electromechanical capacitor and a superconducting qubit, our results reveal the possibility of tunable forces between the capacitor plates, or the level shifts of the qubit, respectively. Our analysis suggests an alternative route towards the exploration of Casimir-like fluctuation potentials, namely, by characterizing and measuring them as a function of parameters of the environment. Such tunable potentials may be useful for future nanoelectromechanical and quantum technologies.","abstract_source_suggest":{"input":"arXiv"}}],"primary_arxiv_category":["quant-ph"],"titles":[{"source":"arXiv","title":"Electronic zero-point fluctuation forces inside circuit components"}],"facet_author_name":["1974218_Ephraim Shahmoon","1000555_Ulf Leonhardt"],"core":true,"license":[{"license":"arXiv nonexclusive-distrib 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Refractive-index profile $n(z)$ of a planar material where the first derivative of $n$ jumps by $1/b$ at the edge to free space with $n=1$. Equation (\\ref{result}) describes the Casimir stress near the edge with $a$ being the distance from the edge. The dotted line indicates the Beltrami profile of Eq.~(\\ref{beltrami}), fitting the actual profile at the edge, employed to calculate the stress analytically. }","label":"softwall","source":"arxiv","key":"b302852b5d936bc1353b82d751fcf544","url":"https://inspirehep.net/files/b302852b5d936bc1353b82d751fcf544"},{"filename":"fig2.png","material":"preprint","caption":"\\small{ Casimir stress. Numerical computation (dots) of the Casimir stress $\\sigma_{zz}$ for the profile $\\varepsilon(z)$ of the electric permittivity shown (grey curve), $\\mu=1$. The solid black curve shows the sum of our formula for the stress near each edge, Eq.~(\\ref{final}), in excellent agreement with the numerical results near the edges. The stress is zero in the constant parts of the profile. We employed the profile \\cite{PXL} $\\varepsilon=\\epsilon^z$ with $\\epsilon=(\\kappa^2+e\\kappa_0^2)/(\\kappa^2+\\kappa_0^2)$ for $0<z<1$ and constant profiles outside. It includes Lorentzian-type dispersion for imaginary wavenumbers with real resonance at $\\kappa_0=200$ (in the shown profile we put $\\kappa=0$). Dispersion is necessary for the convergence of the Casimir stress \\cite{Grin}. }","label":"stressfigure","source":"arxiv","key":"e4c7fe248a607a45a8a5f6f992324834","url":"https://inspirehep.net/files/e4c7fe248a607a45a8a5f6f992324834"}],"legacy_version":"20200528222544.0","inspire_categories":[{"term":"General Physics"},{"term":"Quantum Physics","source":"arxiv"}],"first_author":{"full_name":"Griniasty, Itay","last_name":"Griniasty","first_name":"Itay","recid":2216339},"control_number":1635588,"dois":[{"source":"APS","value":"10.1103/PhysRevB.96.205418"},{"value":"10.1103/PhysRevB.96.205418"},{"material":"publication","source":"arXiv","value":"10.1103/PhysRevB.96.205418"}],"document_type":["article"],"texkeys":["Griniasty:2017iix"],"abstracts":[{"source":"APS","value":"The Casimir force between macroscopic bodies is well understood, but not the Casimir stress inside bodies. Suppose empty space or a uniform medium meets a soft wall where the refractive index is continuous but its derivative jumps. For this situation we predict a characteristic power law for the stress inside the soft wall and close to its edges. Our result shows that such edges are not tolerated in the aggregation of liquids at surfaces, regardless whether the liquid is attracted or repelled.","abstract_source_suggest":{"input":"APS"}},{"source":"arXiv","value":"The Casimir force between macroscopic bodies is well understood, but not the Casimir stress inside bodies. Suppose empty space or a uniform medium meets a soft wall where the refractive index is continuous but its derivative jumps. For this situation we predict a characteristic power law for the stress inside the soft wall and close to its edges. Our result shows that such edges are not tolerated in the aggregation of liquids at surfaces, regardless whether the liquid is attracted or repelled.","abstract_source_suggest":{"input":"arXiv"}}],"primary_arxiv_category":["quant-ph"],"titles":[{"source":"APS","title":"Casimir stress in materials: Hard divergency at soft walls"},{"source":"arXiv","title":"Casimir stress in materials: hard divergency at soft walls"}],"imprints":[{"date":"2017-11-10"}],"curated":false},"updated":"2025-10-14T08:21:08.067066+00:00","links":{"bibtex":"https://inspirehep.net/api/literature/1635588?format=bibtex","latex-eu":"https://inspirehep.net/api/literature/1635588?format=latex-eu","latex-us":"https://inspirehep.net/api/literature/1635588?format=latex-us","json":"https://inspirehep.net/api/literature/1635588?format=json","json-expanded":"https://inspirehep.net/api/literature/1635588?format=json-expanded","cv":"https://inspirehep.net/api/literature/1635588?format=cv","citations":"https://inspirehep.net/api/literature/?q=refersto%3Arecid%3A1635588"}},{"id":"3043147","created":"2025-10-03T10:41:23.868672+00:00","metadata":{"citation_count":3,"authors":[{"raw_affiliations":[{"value":"Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100, Israel"}],"full_name_unicode_normalized":"avni, yael","full_name":"Avni, Yael","record":{"$ref":"https://inspirehep.net/api/authors/2209740"},"ids":[{"schema":"INSPIRE BAI","value":"Y.Avni.1"}],"last_name":"Avni","uuid":"48e1871f-9060-4a65-a9e1-db7f03882005","first_name":"Yael","recid":2209740},{"raw_affiliations":[{"value":"Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100, Israel"}],"full_name_unicode_normalized":"leonhardt, ulf","full_name":"Leonhardt, Ulf","record":{"$ref":"https://inspirehep.net/api/authors/1000555"},"ids":[{"schema":"INSPIRE BAI","value":"U.Leonhardt.1"}],"last_name":"Leonhardt","uuid":"4c829c8a-abde-46c8-8d33-b6f3afce9c2b","first_name":"Ulf","recid":1000555}],"citation_count_without_self_citations":2,"citeable":true,"$schema":"https://inspirehep.net/schemas/records/hep.json","references":[{"reference":{"label":"1","publication_info":{"journal_volume":"115","artid":"1","year":1978,"page_start":"1","journal_title":"Annals Phys."},"authors":[{"full_name":"Schwinger, J."},{"full_name":"DeRaad, L.L."},{"full_name":"Milton, K.A."}]},"raw_refs":[{"schema":"text","source":"arXiv","value":"[1] J. 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Part II: Functions of Positive Integer Order (Cambridge University Press, 1966)."}]}],"referenced_authors_bais":["S.Y.Buhmann.3","L.P.Pitaevskii.1","U.Leonhardt.1","M.T.H.Reid.1","U.Mohideen.1","A.Chodos.1","D.Polder.1","Noah.M.Graham.1","Robert.L.Jaffe.1","M.Kardar.1","L.L.DeRaad.Jr.1","G.Barton.1","T.G.Philbin.3","E.M.Lifshitz.1","O.Kenneth.1","B.Duplantier.2","K.Kirsten.1","T.G.Philbin.2","J.L.White.1","I.E.Dzyaloshinskii.2","Steven.K.Lamoreaux.1","Timothy.H.Boyer.1","R.Balian.1","D.G.Welsch.1","M.Bordag.1","Kenneth.A.Johnson.1","Charles.B.Thorn.1","I.G.Pirozhenko.1","Chuan.Sheng.Xiong.1","F.Capasso.1","T.Emig.1","H.B.G.Casimir.1","V.F.Weisskopf.1","S.G.Johnson.1","Y.J.Ng.2","I.H.Brevik.1","Anushree.Roy.2","S.J.Rahi.2","V.N.Marachevsky.1","Julian.Seymour.Schwinger.1","I.Klich.1","K.A.Milton.1","V.V.Nesterenko.1","A.W.Rodriguez.1","D.V.Vassilevich.1","I.Griniasty.1"],"figures":[{"filename":"fig1.png","material":"preprint","caption":"\\small Dielectric sphere of radius $a$ surrounded by dielectric background. The sphere is subject to pressure arising from vacuum fluctuations. The dielectric properties of the sphere and the background are incorporated in their permittivity and permeability ($\\epsilon$ and $\\mu$ respectively), which determine the response of the materials to vacuum fluctuations.","label":"sphere","source":"arxiv","key":"b48af05149571559677378d6a7fdf8d8","url":"https://inspirehep.net/files/b48af05149571559677378d6a7fdf8d8"},{"filename":"fig2.png","material":"preprint","caption":"\\small A conducting spherical shell can be viewed as the sum over two cases: a vacuum cavity in a conducting background and a conducting sphere in vacuum.","label":"sum","source":"arxiv","key":"7fa57d3abc14e657644d3bd3fc223177","url":"https://inspirehep.net/files/7fa57d3abc14e657644d3bd3fc223177"},{"filename":"fig3.png","material":"preprint","caption":"\\small{$F_m$ as a function of $\\epsilon$. Gray: $\\epsilon_2=\\mu_{1,2}=1$, $\\epsilon_1=\\epsilon$. White: $\\epsilon_1=\\mu_{1,2}=1$, $\\epsilon_2=\\epsilon$. Black: The sum of the gray and white points, which is meaningful only in the limit $\\epsilon \\to \\infty$. Dashed: the limit of a perfectly conducting spherical shell: $F_m=0.04618 \\hbar c/a^2$.}","label":"force","source":"arxiv","key":"75c70365276e0f992ab754b5cb875158","url":"https://inspirehep.net/files/75c70365276e0f992ab754b5cb875158"},{"filename":"fig4.png","material":"preprint","caption":"\\small{$F_m$ in a dilute dielectric sphere inside vacuum: $\\epsilon_1=\\epsilon\\approx1,\\epsilon_2=\\mu_{1,2}=1$ }","label":"dilute","source":"arxiv","key":"69feea160e198ac23ce9320aab6a5abc","url":"https://inspirehep.net/files/69feea160e198ac23ce9320aab6a5abc"},{"filename":"fig5a.png","material":"preprint","caption":"\\small{Direct interactions versus scattering. a: diagram illustrating the physical picture of the Casimir force as the result of direct molecular interactions. In the dilute limit, a given molecule (white point) interacts with each of the other molecules (other white points) by Casimir-Polder forces; triple or higher interactions can be neglected. In this picture the Casimir stress would depend quadratically on the density, {\\it i.e.} quadratically on $\\epsilon-1$. b: diagram showing the scattering of a wave emitted by the molecule (white point) at the boundary of the medium. The reflected wave gives rise to the Casimir stress. As one reflection already generates stress, the Casimir stress should scale linearly with $\\epsilon-1$ in the dilute limit, which does agree with our numerical results. The figure shows the imaginary part of the difference between a wave in the medium and the outgoing wave (for a scalar wave in 2D, for simplicity).}","label":"reflections","source":"arxiv","key":"d94fc30df9644ecd749575b3bcb6cb0a","url":"https://inspirehep.net/files/d94fc30df9644ecd749575b3bcb6cb0a"},{"filename":"fig5b.png","material":"preprint","caption":"\\small{Direct interactions versus scattering. a: diagram illustrating the physical picture of the Casimir force as the result of direct molecular interactions. In the dilute limit, a given molecule (white point) interacts with each of the other molecules (other white points) by Casimir-Polder forces; triple or higher interactions can be neglected. In this picture the Casimir stress would depend quadratically on the density, {\\it i.e.} quadratically on $\\epsilon-1$. b: diagram showing the scattering of a wave emitted by the molecule (white point) at the boundary of the medium. The reflected wave gives rise to the Casimir stress. As one reflection already generates stress, the Casimir stress should scale linearly with $\\epsilon-1$ in the dilute limit, which does agree with our numerical results. The figure shows the imaginary part of the difference between a wave in the medium and the outgoing wave (for a scalar wave in 2D, for simplicity).}","label":"reflections","source":"arxiv","key":"3c58dfce56bf2eace4ba711c63134d08","url":"https://inspirehep.net/files/3c58dfce56bf2eace4ba711c63134d08"},{"filename":"fig6a.png","material":"preprint","caption":"\\small{ Convergence of the fit ({\\bf a}) and of the asymptotic expansion ({\\bf b}). The figures show $F_m$ with the parameters $\\epsilon_2=\\mu_{1,2}=1$, $\\epsilon_1=\\epsilon$ as a function of $\\epsilon$. In ({\\bf a}) $N$ is the highest order taken in the linear fit: $y=\\sum_{n=-3}^{N}a_{n}^{\\mbox{i}}\\delta^{n}+\\sum_{n=0}^{N}b_{n}^{\\mbox{\\ensuremath{\\text{i}}}}\\delta^{n}\\log\\left(\\delta\\right)$ while in ({\\bf b}) $N$ is the highest order taken in the asymptotic expansion.}","label":"convergence2","source":"arxiv","key":"61ba79f468bcb4c8c0575c5e50d2327c","url":"https://inspirehep.net/files/61ba79f468bcb4c8c0575c5e50d2327c"},{"filename":"fig6b.png","material":"preprint","caption":"\\small{ Convergence of the fit ({\\bf a}) and of the asymptotic expansion ({\\bf b}). The figures show $F_m$ with the parameters $\\epsilon_2=\\mu_{1,2}=1$, $\\epsilon_1=\\epsilon$ as a function of $\\epsilon$. In ({\\bf a}) $N$ is the highest order taken in the linear fit: $y=\\sum_{n=-3}^{N}a_{n}^{\\mbox{i}}\\delta^{n}+\\sum_{n=0}^{N}b_{n}^{\\mbox{\\ensuremath{\\text{i}}}}\\delta^{n}\\log\\left(\\delta\\right)$ while in ({\\bf b}) $N$ is the highest order taken in the asymptotic expansion.}","label":"convergence2","source":"arxiv","key":"ee9c8766f157043d83feedeb89e2e1f7","url":"https://inspirehep.net/files/ee9c8766f157043d83feedeb89e2e1f7"},{"filename":"fig7.png","material":"preprint","caption":"\\small{$F_m$ as a function of $\\epsilon$ with the parameter fit of Eq. (\\ref{fit2}), $\\delta$, replaced by $\\alpha \\delta$. From bright to dark: $\\alpha=1/2, 1, 2$. Full line: $\\epsilon_2=\\mu_{1,2}=1$, $\\epsilon_1=\\epsilon$. Dashed line: $\\epsilon_1=\\mu_{1,2}=1$, $\\epsilon_2=\\epsilon$.}","label":"log","source":"arxiv","key":"cd359ef24cb21920d44159efdc507010","url":"https://inspirehep.net/files/cd359ef24cb21920d44159efdc507010"}],"inspire_categories":[{"term":"Quantum Physics","source":"arxiv"},{"term":"Condensed Matter","source":"arxiv"}],"preprint_date":"2018-03-18","author_count":2,"first_author":{"full_name":"Avni, Yael","last_name":"Avni","first_name":"Yael","recid":2209740},"control_number":3043147,"dois":[{"material":"publication","source":"arXiv","value":"10.1016/j.aop.2018.06.002"}],"earliest_date":"2018-03-18","document_type":["article"],"texkeys":["Avni:2018rbc"],"abstracts":[{"source":"arXiv","value":"The dielectric sphere has been an important test case for understanding and calculating the vacuum force of a dielectric body onto itself. Here we develop a method for computing this force in homogeneous spheres of arbitrary dielectric properties embedded in arbitrary homogeneous backgrounds, assuming only that both materials are isotropic and dispersionless. Our results agree with known special cases; most notably we reproduce the prediction of Boyer and Schwinger et al. of a repulsive Casimir force of a perfectly reflecting shell. Our results disagree with the literature in the dilute limit. We argue that Casimir forces can not be regarded as due to pair-wise Casimir-Polder interactions, but rather due to reflections of virtual electromagnetic waves.","abstract_source_suggest":{"input":"arXiv"}}],"primary_arxiv_category":["quant-ph"],"titles":[{"source":"arXiv","title":"Casimir self-stress in a dielectric sphere"}],"facet_author_name":["2209740_Y. 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Space-time diagram of light-ray trajectories near the horizon given by Eq. \\eqref{geoeq}. Straight lines (dashed orange) represent rays traveling with the fluid (copropagating waves), for which there is nothing special in the horizon. Curved lines (solid blue) represent rays traveling against the fluid (counterpropagating waves) and they are split into two at the horizon. The center black-line is the horizon. The radius $r$ is written in terms of $r_S^{-1}$ units.","source":"arxiv","label":"geodesics","key":"17f6170519f02c2caea239501f1f80f4","url":"https://inspirehep.net/files/17f6170519f02c2caea239501f1f80f4"},{"filename":"stless.png","material":"preprint","caption":"(Color online). Space-time diagram of light rays near the horizon for the velocity profile in Eq. \\eqref{velprof} for two cases: dispersionless (up) and dispersion $c(k)$ from Eq. \\eqref{dispfluid} (down). In the first case the horizon is well defined, but in the second one is ``fuzzy'' as it depends on $k$. We show three pairs of rays that conserve $\\omega-uk$, one with positive (blue) and the other with negative (green) frequency.","source":"arxiv","label":"sts","key":"af98617fd61830c7905cd2a41445843a","url":"https://inspirehep.net/files/af98617fd61830c7905cd2a41445843a"},{"filename":"stdisp.png","material":"preprint","caption":"(Color online). Space-time diagram of light rays near the horizon for the velocity profile in Eq. \\eqref{velprof} for two cases: dispersionless (up) and dispersion $c(k)$ from Eq. \\eqref{dispfluid} (down). In the first case the horizon is well defined, but in the second one is ``fuzzy'' as it depends on $k$. We show three pairs of rays that conserve $\\omega-uk$, one with positive (blue) and the other with negative (green) frequency.","source":"arxiv","label":"sts","key":"f0449fd6c2a4e3c872f59d20fe59bd71","url":"https://inspirehep.net/files/f0449fd6c2a4e3c872f59d20fe59bd71"},{"filename":"fts.png","material":"preprint","caption":"(Color online). The Fourier transform of the sech$(t)$ pulse (solid blue), the real part of the half Fourier transforms (dashed orange), the imaginary parts of left- (dot-dashed green) and right- (dotted red) Fourier transforms.","source":"arxiv","label":"figfts","key":"26bba9f083f56c0bdfd7608ee4708b92","url":"https://inspirehep.net/files/26bba9f083f56c0bdfd7608ee4708b92"},{"filename":"beta.png","material":"preprint","caption":"(Color online). Dispersion relation $\\beta(\\omega)$ for counterpropagating waves using the model in Eq. \\eqref{beta} with two terms (solid blue). We also show the negative of this function (dashed red) that is useful to match the negative frequencies.","source":"arxiv","label":"figbeta","key":"20085202e611c5ffea6f67c04aaffe24","url":"https://inspirehep.net/files/20085202e611c5ffea6f67c04aaffe24"},{"filename":"wpwpoints.png","material":"preprint","caption":"(Color online). Dispersion relation in the comoving frame $\\omega'=\\omega'(\\omega)$ from Eq. \\eqref{wpw} and $\\beta(\\omega)$ from Eq. \\eqref{beta}. We show the function for the copropagating waves (solid blue), its negative (dot-dashed red) to match with negative-frequency waves, and the counterpropagating waves (dashed orange). We also show the two points of interest: the phase horizon ($\\omega_z,0$) and the group horizon ($\\omega_h,\\omega_h'$).","source":"arxiv","label":"figwprime2","key":"2e4910e4ea93ec9e74ddba0c42745690","url":"https://inspirehep.net/files/2e4910e4ea93ec9e74ddba0c42745690"},{"filename":"wpwfull.png","material":"preprint","caption":"(Color online). The dispersion relation for counterpropagating (solid blue) and copropagating waves (dashed orange); the negative of the counterpropagating (dot-dashed red) dispersion is also plotted as it indicates the matching with the negative frequency. The horizontal line (dotted green) represents the conservation of $\\omega'$ and the points shown satisfy the matching conditions for the unperturbed system. The labels 1, 2, 3, and $3'$ correspond to the identification of the modes for the numerical solution.","source":"arxiv","label":"figwpwfull","key":"f063d2e4500ffbced7dd64df7f803dc7","url":"https://inspirehep.net/files/f063d2e4500ffbced7dd64df7f803dc7"},{"filename":"wpwclose.png","material":"preprint","caption":"(Color online). Close up on $\\omega'_h$ from Fig. \\ref{figwpwfull}. The diagonal purple line shows the maximum slope reached by the pulse with $\\delta n_\\text{max}$ and defines the edge of frequencies $\\omega'_\\text{min}$ from the three modes that are able to reach the horizon due to the Kerr effect when we consider the soliton. This range is shown in green shadow.","source":"arxiv","label":"figwpwclose","key":"267f7b14e6c002902261a58dc0cf1d79","url":"https://inspirehep.net/files/267f7b14e6c002902261a58dc0cf1d79"},{"filename":"specfullw.png","material":"preprint","caption":"(Color online). Full Hawking spectrum for the dispersion. The peaks are in $\\omega_h$ and $\\omega_{\\text{max1}}$. The vertical gray lines mark the shown frequencies, the lines on the sides of $\\omega_h$ are $\\omega_{\\text{min3}}$ and $\\omega_{\\text{min3'}}$. Also, to the right of $\\omega_\\text{max2}$ is $\\omega_\\text{min2}$ and to the left of $\\omega_\\text{max1}$ is $\\omega_\\text{min1}$, both indistinguishable from this scale. These lines limit the region for creation of Hawking radiation.","source":"arxiv","label":"fighsfull","key":"8cff4e0af342e0b43aada1ea13a61fef","url":"https://inspirehep.net/files/8cff4e0af342e0b43aada1ea13a61fef"},{"filename":"specwh.png","material":"preprint","caption":"(Color online). Close up of the Hawking spectrum around the horizon in $\\omega_h$ and around the negative frequency horizon in $\\omega_\\text{max1}$. In both cases we observe that the particle production dips to zero exactly at the horizon. The dashed orange lines correspond to the same arbitrary value of $\\omega'$ and they will be correlated.","source":"arxiv","label":"fighsclose","key":"04c02788546b3e0908fce0e9abb0041e","url":"https://inspirehep.net/files/04c02788546b3e0908fce0e9abb0041e"},{"filename":"specwhmax2.png","material":"preprint","caption":"(Color online). Close up of the Hawking spectrum around the horizon in $\\omega_h$ and around the negative frequency horizon in $\\omega_\\text{max1}$. In both cases we observe that the particle production dips to zero exactly at the horizon. The dashed orange lines correspond to the same arbitrary value of $\\omega'$ and they will be correlated.","source":"arxiv","label":"fighsclose","key":"65447fb7e402a4cc9cf1dd50a3444947","url":"https://inspirehep.net/files/65447fb7e402a4cc9cf1dd50a3444947"},{"filename":"norm.png","material":"preprint","caption":"(Color online). Norm conservation. The positive-norm (solid blue) is the sum of the norm of modes 2, 3, and $3'$, the negative norm (dashed green) is the norm of mode 1. We also show the sum of both of them and we check the norm conservation (dotted red). The norm is normalized according to the maximum (close to the horizon).","source":"arxiv","label":"fignorm","key":"fe3bda9b387ccffbcdef393e0178c011","url":"https://inspirehep.net/files/fe3bda9b387ccffbcdef393e0178c011"},{"filename":"error.png","material":"preprint","caption":"(Color online). Relative difference between the positive- and negative-norm modes (relative error) in terms of $\\omega'$. As expected, the maximum value is at the horizon and it is less than 1\\%.","source":"arxiv","label":"figerror","key":"509225343fd6adeffeba21bdff7f043c","url":"https://inspirehep.net/files/509225343fd6adeffeba21bdff7f043c"}],"first_author":{"emails":["dbermudez@fis.cinvestav.mx"],"affiliations_identifiers":[{"schema":"ROR","value":"https://ror.org/059sp8j34"}],"full_name":"Bermudez, David","ids":[{"schema":"INSPIRE ID","value":"INSPIRE-00353448"},{"schema":"ORCID","value":"0000-0002-2977-0303"},{"schema":"INSPIRE BAI","value":"D.Bermudez.2"}],"last_name":"Bermudez","first_name":"David","recid":1078473},"control_number":1416981,"dois":[{"material":"publication","source":"arXiv","value":"10.1103/PhysRevA.93.053820"},{"value":"10.1103/PhysRevA.93.053820"}],"document_type":["article"],"texkeys":["Bermudez:2016hbl"],"abstracts":[{"source":"arXiv","value":"Hawking radiation has been regarded as a more general phenomenon than in gravitational physics, in particular in laboratory analogs of the event horizon. Here we consider the fiber-optical analog of the event horizon, where intense light pulses in fibers establish horizons for probe light. Then, we calculate the Hawking spectrum in an experimentally realizable system. We found that the Hawking radiation is peaked around group-velocity horizons in which the speed of the pulse matches the group velocity of the probe light. The radiation nearly vanishes at the phase horizon where the speed of the pulse matches the phase velocity of light.","abstract_source_suggest":{"input":"arXiv"}}],"primary_arxiv_category":["gr-qc"],"titles":[{"source":"arXiv","title":"Hawking spectrum for a fiber-optical analog of the event horizon"},{"source":"arXiv","title":"Hawking spectrum for a fiber-optical analogue of the event horizon"}],"imprints":[{"date":"2016-05-16"}],"curated":true},"updated":"2026-08-04T22:41:10.300278+00:00","links":{"bibtex":"https://inspirehep.net/api/literature/1416981?format=bibtex","latex-eu":"https://inspirehep.net/api/literature/1416981?format=latex-eu","latex-us":"https://inspirehep.net/api/literature/1416981?format=latex-us","json":"https://inspirehep.net/api/literature/1416981?format=json","json-expanded":"https://inspirehep.net/api/literature/1416981?format=json-expanded","cv":"https://inspirehep.net/api/literature/1416981?format=cv","citations":"https://inspirehep.net/api/literature/?q=refersto%3Arecid%3A1416981"}},{"id":"824291","created":"2009-06-29T00:00:00+00:00","metadata":{"citation_count":6,"publication_info":[{"journal_volume":"8","page_end":"642","year":2009,"journal_record":{"$ref":"https://inspirehep.net/api/journals/1212542"},"page_start":"639","journal_title":"Nature Materials"}],"authors":[{"affiliations_identifiers":[{"schema":"ROR","value":"https://ror.org/01tgyzw49"}],"full_name_unicode_normalized":"ma, yun gui","full_name":"Ma, Yun Gui","curated_relation":true,"record":{"$ref":"https://inspirehep.net/api/authors/1600624"},"last_name":"Ma","ids":[{"schema":"INSPIRE BAI","value":"Yun.Gui.Ma.1"}],"affiliations":[{"record":{"$ref":"https://inspirehep.net/api/institutions/904194"},"value":"Singapore Natl. 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Ong","2576264_Tomas Tyc"],"_oai":{"sets":["Literature"],"id":"oai:inspirehep.net:824291","updated":"2023-03-07T02:21:33.622009"},"journal_title_variants":["Nature Materials"],"arxiv_eprints":[{"categories":["physics.optics"],"value":"0906.5214"}],"referenced_authors_bais":["T.G.Philbin.2","U.Leonhardt.1","C.K.Ong.2","L.L.Zhao.1"],"figures":[{"filename":"fig1a.png","caption":"\\small {\\bf $|$ Eaton lenses.} {\\bf a}, Spherical lens. {\\bf b}, Cylindrical lens. Artist's impression of the retroreflection of light that carries an image, the letter ``E'' for ``Eaton''. In the outgoing light, the image is inverted, but preserved (in a: flipped and upside down, in b: flipped). The implementation of an Eaton lens would require a singularity in the refractive index profile where the index tends to infinity, unless the singularity is transmuted into a harmless topological defect, as we demonstrate in this paper for the cylindrical lens with metamaterials for microwaves.","source":"arxiv","key":"e0975a6398fae66e0f9d6bd6e8823dd6","url":"https://inspirehep.net/files/e0975a6398fae66e0f9d6bd6e8823dd6"},{"filename":"fig1b.png","caption":"\\small {\\bf $|$ Eaton lenses.} {\\bf a}, Spherical lens. {\\bf b}, Cylindrical lens. Artist's impression of the retroreflection of light that carries an image, the letter ``E'' for ``Eaton''. In the outgoing light, the image is inverted, but preserved (in a: flipped and upside down, in b: flipped). The implementation of an Eaton lens would require a singularity in the refractive index profile where the index tends to infinity, unless the singularity is transmuted into a harmless topological defect, as we demonstrate in this paper for the cylindrical lens with metamaterials for microwaves.","source":"arxiv","key":"f8ae623d94595432a5c88e3a99397d53","url":"https://inspirehep.net/files/f8ae623d94595432a5c88e3a99397d53"},{"filename":"fig2.png","caption":"\\small{\\bf $|$ Simulation of Eaton lenses.} The left pictures show the distribution of the electric field at the original (a) and transformed Eaton lenses (b) and (c) with dielectric functions (\\ref{cylinder}) and (\\ref{rescaled}), respectively; the right pictures show the corresponding biscattering diagrams. The dashed circles in the left picture mark the boundary of the device at radius $a$ ($40\\rm{mm}$), the dotted lines refer to an absorbing sheet that separates the incident and reflected electromagnetic waves with their direction indicated by the dotted arrows. The wavelength is $a/4$ and the scale is in mm. The biscattering diagrams refer to the electric field infinitely far away from the device. They display the ratio of the magnitude of the electric field as a function of angle, normalized by the largest value.","source":"arxiv","key":"d0bdaad2e399cab1132ddc29d7e5002c","url":"https://inspirehep.net/files/d0bdaad2e399cab1132ddc29d7e5002c"},{"filename":"fig3.png","caption":"\\small {\\bf $|$ The device.} The split-ring resonators constitute a metamaterial for microwave radiation with the designed radial magnetic permeability (\\ref{rescaled}). The rings were then filled with a white dielectric powder that generates the required electric permittivity of $n_0^2$ (not shown here).","source":"arxiv","key":"733e371e3103c1ee239e88a0a893211d","url":"https://inspirehep.net/files/733e371e3103c1ee239e88a0a893211d"},{"filename":"fig4.png","caption":"\\small {\\bf $|$ Effective electromagnetic properties.} The blue curve shows the index profile (\\ref{eaton}) of the original Eaton lens as a function of the radius $r$, the other curves display the rescaled dielectric functions (\\ref{rescaled}) of the transmuted Eaton lens. The inset shows $\\mu_r$ with magnified scale. The symbols are the dielectric functions calculated for the corresponding layers of the metamaterial.","source":"arxiv","key":"85e6a0f21451c0513d68a49aaf75369c","url":"https://inspirehep.net/files/85e6a0f21451c0513d68a49aaf75369c"},{"filename":"fig5.png","caption":"\\small {\\bf $|$ Measurement results (a) compared with simulation (b)}. Description as for the left pictures of Fig.\\ 2, except that here the wavelength is $34 \\mathrm{mm}$ ($0.85a$).","source":"arxiv","key":"c25687d4ea81a50006042fddb7f9640f","url":"https://inspirehep.net/files/c25687d4ea81a50006042fddb7f9640f"}],"legacy_version":"20160326145931.0","inspire_categories":[{"term":"General Physics"}],"first_author":{"affiliations_identifiers":[{"schema":"ROR","value":"https://ror.org/01tgyzw49"}],"full_name":"Ma, Yun Gui","last_name":"Ma","first_name":"Yun Gui","recid":1600624},"control_number":824291,"dois":[{"value":"10.1038/nmat2489"}],"document_type":["article"],"texkeys":["Ma:2009vg"],"abstracts":[{"source":"arXiv","value":"In the field of transformation optics, metamaterials mimic the effect of coordinate transformations on electromagnetic waves, creating the illusion that the waves are propagating through a virtual space. Transforming space by appropriately designed materials makes devices possible that have been deemed impossible. In particular, transformation optics has led to the demonstration of invisibility cloaking for microwaves, surface plasmons and infrared light. Here we report the achievement of another 'impossible task'. We implement, for microwaves, a device that would normally require a dielectric singularity, an infinity in the refractive index. We transmute a singularity in virtual space into a mere topological defect in a real metamaterial. In particular, we demonstrate an omnidirectional retroreflector, a device for faithfully reflecting images and for creating high visibility, from all directions. Our method is robust, potentially broadband and similar techniques could be applied for visible light.","abstract_source_suggest":{"input":"arXiv"}}],"primary_arxiv_category":["physics.optics"],"titles":[{"title":"An Omnidirectional retroreflector based on the transmutation of dielectric singularities"},{"source":"arXiv","title":"An omnidirectional retroreflector based on the transmutation of dielectric singularities"}],"curated":true},"updated":"2023-03-07T02:21:33.622009+00:00","links":{"bibtex":"https://inspirehep.net/api/literature/824291?format=bibtex","latex-eu":"https://inspirehep.net/api/literature/824291?format=latex-eu","latex-us":"https://inspirehep.net/api/literature/824291?format=latex-us","json":"https://inspirehep.net/api/literature/824291?format=json","json-expanded":"https://inspirehep.net/api/literature/824291?format=json-expanded","cv":"https://inspirehep.net/api/literature/824291?format=cv","citations":"https://inspirehep.net/api/literature/?q=refersto%3Arecid%3A824291"}},{"id":"1811142","created":"2020-08-12T00:00:00+00:00","metadata":{"citation_count":21,"publication_info":[{"journal_volume":"507","pubinfo_freetext":"MNRAS 507, 3473 (2021)","artid":"3473","material":"publication","page_end":"3485","year":2021,"journal_record":{"$ref":"https://inspirehep.net/api/journals/1214577"},"page_start":"3473","journal_issue":"3","journal_title":"Mon.Not.Roy.Astron.Soc."}],"documents":[{"filename":"document","fulltext":true,"key":"35b0d5ac87d58373ad36ba8f481d163d","url":"https://inspirehep.net/files/35b0d5ac87d58373ad36ba8f481d163d"}],"authors":[{"raw_affiliations":[{"value":"Weizmann Institute of Science, Rehovot 7610001, Israel"}],"full_name_unicode_normalized":"berechya, dror","full_name":"Berechya, Dror","record":{"$ref":"https://inspirehep.net/api/authors/1897202"},"affiliations":[{"record":{"$ref":"https://inspirehep.net/api/institutions/903342"},"value":"Weizmann Inst."}],"last_name":"Berechya","ids":[{"schema":"INSPIRE BAI","value":"D.Berechya.1"}],"signature_block":"BARACHd","uuid":"786c9653-fc0d-4c99-b02f-d15706f2b1f3","first_name":"Dror","recid":1897202},{"raw_affiliations":[{"value":"Weizmann Institute of Science, Rehovot 7610001, Israel"}],"full_name_unicode_normalized":"leonhardt, ulf","full_name":"Leonhardt, Ulf","record":{"$ref":"https://inspirehep.net/api/authors/1000555"},"affiliations":[{"record":{"$ref":"https://inspirehep.net/api/institutions/903342"},"value":"Weizmann Inst."}],"last_name":"Leonhardt","ids":[{"schema":"INSPIRE BAI","value":"U.Leonhardt.1"}],"signature_block":"LANARDu","uuid":"81c8eff9-b7db-461f-b534-4e38da369766","first_name":"Ulf","recid":1000555}],"citation_count_without_self_citations":15,"citeable":true,"$schema":"https://inspirehep.net/schemas/records/hep.json","keywords":[{"source":"author","value":"dark energy"},{"schema":"INSPIRE","value":"force: Casimir"},{"schema":"INSPIRE","value":"space-time: expansion"},{"schema":"INSPIRE","value":"Hubble constant"},{"schema":"INSPIRE","value":"cosmic background radiation"},{"schema":"INSPIRE","value":"cosmological constant"},{"schema":"INSPIRE","value":"cosmological model"},{"schema":"INSPIRE","value":"equation of state"},{"schema":"INSPIRE","value":"time dependence"},{"schema":"INSPIRE","value":"redshift"},{"schema":"INSPIRE","value":"tension"},{"schema":"INSPIRE","value":"optical"},{"schema":"INSPIRE","value":"vacuum state: quantum"}],"references":[{"reference":{"dois":["10.1051/0004-6361/201935638"],"publication_info":{"journal_volume":"629","artid":"A85","year":2019,"journal_record":{"$ref":"https://inspirehep.net/api/journals/1214902"},"page_start":"A85","journal_title":"Astron.Astrophys."},"misc":["d. 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.Riess.1","G.Savini.1","E.Kourkchi.1","J.B.Melin.1","K.S.Dawson.1","F.Perrotta.1","Paul.C.W.Davies.1","S.Alam.4","S.Gratton.1","A.Renzi.1","C.Renault.1","V.A.Parsegian.1","F.Villa.2","N.Hand.1","Laurence.Perotto.1","Y.Xia.1","Bradley.E.Tucker.1","S.R.Hildebrandt.1","H.K.Eriksen.1","Ryan.J.Foley.1","A.N.Lasenby.1","Pauline.Zarrouk.1","J.R.Neeley.1","P.Vielva.1","D.Molinari.1","H.U.Norgaard.Nielsen.1","F.Paci.3","A.Gruppuso.1","F.Forastieri.1","C.Dickinson.1","Douglas.P.Finkbeiner.1","I.B.Thompson.4","Jiamin.Hou.1","Dale.Kocevski.1","Francois.R.Bouchet.1","J.R.Fergusson.1","B.Hayden.2","Fabio.Finelli.1","K.I.Clubb.4","Duncan.J.Scott.1","A.De.Rosa.2","Hiranya.Vajramani.Peiris.1","L.Rizzi.2","T.Trombetti.4","Joanna.Dunkley.1"],"figures":[{"filename":"fig1.png","material":"preprint","caption":"$\\Omega_{\\infty} h^2 \\equiv \\displaystyle \\lim_{a \\rightarrow \\infty}\\Omega_{LC}h^2$ as a function of $\\al$ in the range of interest. This relationship results when demanding that Lifshitz cosmology preserves $D_M$ (\\EqRef{\\ref{fixing_the_integration_constant}}), and it is calculated according to \\EqRef{\\ref{fitting_condition_for_delta}} with $\\omega_m^P = 0.1430$ and $\\omega_\\Lambda^P = 0.3107$ from Ref.~\\cite{planck_collaboration_planck_2020}. The bands show the $\\pm 1 \\sigma$ (dark gray) and $\\pm 2 \\sigma$ (light gray) errors in $\\Omega_{\\infty} h^2$ as estimated by propagating the errors in $D_M^{(\\Lambda \\mathrm{CDM})}$ (see Appendix~\\ref{Late_universe}). The two realizations of Lifshitz cosmology considered in this paper are also shown: M1 (black and yellow point), the theoretical prediction for electromagnetic contribution alone with a sharp cut--off at exactly the Planck length, $\\alpha_\\Lambda^{M1} = \\alpha_\\Lambda^{TH} = (9\\pi)^{-1}$ and M2 (black point), $\\alpha_\\Lambda^{M2} = 0.0225$.","label":"OmegaInfVSalpha","source":"arxiv","key":"62c3e79636a2d9bb2c03d4c0b6138535","url":"https://inspirehep.net/files/62c3e79636a2d9bb2c03d4c0b6138535"},{"filename":"fig2.png","material":"preprint","caption":"$H_0$ in units of $\\mathrm{km \\: s^{-1} \\: \\! Mpc^{-1}}$ as a function of $\\al$ in the range of interest. The bands show the $\\pm 1 \\sigma$ (dark gray) and $\\pm 2 \\sigma$ (light gray) errors in $H_0$ obtained by propagating the errors in $\\Omega_{\\infty} h^2$. The theory points M1 and M2 are as in Fig.~\\ref{OmegaInfVSalpha}. We also show several local measurements of $H_0$, done by several independent groups using several independent methods: Cepheids - SN Ia ($73.2\\pm1.3$ by \\citeauthor{riess_cosmic_2021}, \\citeyear{riess_cosmic_2021} \\cite{riess_cosmic_2021}, SH0ES team), TRGB - SN Ia ($72.1\\pm2.0$ by \\citeauthor{soltis_parallax_2021}, \\citeyear{soltis_parallax_2021} \\cite{soltis_parallax_2021} and $69.6\\pm1.88$ by \\citeauthor{freedman_calibration_2020}, \\citeyear{freedman_calibration_2020} \\cite{freedman_calibration_2020}), Tully Fisher ($76.00\\pm2.55$ by \\citeauthor{kourkchi_cosmicflows-4_2020}, \\citeyear{kourkchi_cosmicflows-4_2020} \\cite{kourkchi_cosmicflows-4_2020}), Surface Brightness Fluctuations (SBF) ($73.3\\pm2.5$ by \\citeauthor{blakeslee_hubble_2021}, \\citeyear{blakeslee_hubble_2021} \\cite{blakeslee_hubble_2021} and $70.5\\pm4.1$ by \\citeauthor{khetan_new_2021}, \\citeyear{khetan_new_2021} \\cite{khetan_new_2021}), SN II ($75.8^{+5.2}_{-4.9}$ by \\citeauthor{dejaeger_measurement_2020}, \\citeyear{dejaeger_measurement_2020} \\cite{dejaeger_measurement_2020}), and Time-delay Lensing ($74.5^{+5.6}_{-6.1}$ and $67.4^{+4.2}_{-3.2}$ by \\citeauthor{birrer_tdcosmo_2020}, \\citeyear{birrer_tdcosmo_2020} \\cite{birrer_tdcosmo_2020}). All the values are in units of $\\mathrm{km \\: s^{-1} \\: \\! Mpc^{-1}}$ and quoted from the compilation in Ref.~\\cite{divalentino_combined_2021}. As can be seen, whatever the actual value of $H_0$ is, Lifshitz cosmology may reproduce the correct value (at least nominally, see the discussion in Sec.~\\ref{The_Hubble_diagram_and_distance_ladders}). The theoretical prediction (M1) is more or less at the middle of the local measurements, and remarkably, it is right on the latest measurement by the SH0ES team (red point).","label":"H0VSalpha","source":"arxiv","key":"921bc8529add5cf9bbcc50de84dde8f0","url":"https://inspirehep.net/files/921bc8529add5cf9bbcc50de84dde8f0"},{"filename":"fig3.png","material":"preprint","caption":"$\\Delta\\mu \\equiv \\mu - \\mu_{\\Lambda \\mathrm{CDM}}$ as a function of $z$. Top panel: Pantheon data \\cite{scolnic_complete_2018} (yellow (unbinned data) and blue (binned data) points) with the reproduced SH0ES absolute magnitude $M_B = -19.244$ from Ref.~\\cite{efstathiou_h0_2021}. The theoretical predictions are also shown: unbroken black cure represents M1, and dashed black curve represents M2. The gray band around each curve shows the $\\pm 1 \\sigma$ errors in $\\Delta\\mu$ obtained by propagating the errors in $\\Omega_{\\infty} h^2$. Bottom panel: The binned Pantheon data are shown with $M_B = -19.330$ (Green) and with $M_B = -19.388$ (Purple), the best $M_B$ in terms of RMSD (\\EqRef{\\ref{RMSD_equation}}) for M1 and M2, respectively.","label":"muVSzFull","source":"arxiv","key":"764b8b1ccbdd4c38e020cafbdb6df3bb","url":"https://inspirehep.net/files/764b8b1ccbdd4c38e020cafbdb6df3bb"},{"filename":"fig4.png","material":"preprint","caption":"$\\Delta[E^{-1}] \\equiv E^{-1} - E^{-1}_{\\Lambda \\mathrm{CDM}}$ as a function of $z$. The six gray points are model--independent measurements of $E^{-1}$ performed by Ref.~\\cite{riess_type_2018} based on SN Ia data alone. The theoretical predictions are also shown: unbroken black cure represents M1, and dashed black curve represents M2. The gray band around each curve shows the $\\pm 1 \\sigma$ errors in $\\Delta[E^{-1}]$ obtained by propagating the errors in $\\Omega_{\\infty} h^2$. Among the six data points, three (at $z = 0.07, 0.35,$ and $0.9$) are situated closer to M1's curve, and the remaining three (at $z = 0.2, 0.55,$ and $1.5$) are situated closer to the \\lcdm{} baseline. M2 lies in between, and it seems to agree with all data points. All in all, Lifshitz cosmology appears to fit the data comparably to \\lcdm{}.","label":"Eofzdata","source":"arxiv","key":"a36c428c55f7b2cacd58e9a1f5266067","url":"https://inspirehep.net/files/a36c428c55f7b2cacd58e9a1f5266067"},{"filename":"fig5.png","material":"preprint","caption":"$H(z)/(1+z)$ in units of $\\mathrm{km \\: s^{-1} \\: \\! Mpc^{-1}}$ as a function of $z$. The theoretical predictions are shown: red curve -- \\lcdm{} and black curves -- Lifshitz cosmology: unbroken -- M1 and dashed -- M2. The gray band around each black curve shows the $\\pm 1 \\sigma$ errors in $H(z)/(1+z)$ obtained by propagating the errors in $\\Omega_{\\infty} h^2$. Also shown are BAO results with $r_d = 147.09 \\mathrm{\\: Mpc}$ at several redshifts from: galaxy correlations in BOSS DR12 \\cite{alam_clustering_2017}, quasar correlation in eBOSS DR16 \\cite{hou_completed_2021}, the correlations of Ly$\\alpha$ absorption in eBOSS DR14 \\cite{agathe_baryon_2019}, and cross--correlation of Ly$\\alpha$ absorption and quasars in eBOSS DR14 \\cite{blomqvist_baryon_2019}. The SH0ES measurement at $z=0$ \\cite{riess_cosmic_2021} is shown as well. While the overall fit of \\lcdm{} to the BAO measurements seems to be somewhat better, the fit of the two Lifshitz cosmology realizations seems to be reasonably acceptable. The point at $z = 0.61$ already disagrees with \\lcdm{}, but more severely so with M2 and even more with M1. The point at $z = 0.38$ agrees with Lifshitz cosmology (M1 and M2) slightly better, and so does the point at $z = 1.48$.","label":"BAOdata","source":"arxiv","key":"bd93cf242365c1b52ce1db30a669ef0f","url":"https://inspirehep.net/files/bd93cf242365c1b52ce1db30a669ef0f"},{"filename":"fig6.png","material":"preprint","caption":"Relative dark energy contribution $f_{de}$ as a function of $z$, as calculated from the approximation of Lifshitz cosmology's dynamics including the early universe. The unbroken curve shows the case M1 and the dashed curve M2. The $\\pm 1 \\sigma$ errors in $f_{de}$ due to errors in $\\Omega_{\\infty} h^2$ are not shown here since they are thinner than the curve's width. Three special times are presented: matter--radiation equality $z_{eq} = 3,402$ \\cite{planck_collaboration_planck_2020} (orange), last--scattering $z_* = 1,089.92$ \\cite{planck_collaboration_planck_2020} (red), and vacuum--matter equality $z_{vm} \\approx 0.29$ (calculated from $f_{de}(z=z_{vm}) = 0.5$) (blue). The early--universe evolution of $f_{de}$, according to Lifshitz cosmology, takes place roughly at the range $223 \\le z \\le 30,350$ for M1 or $388 \\le z \\le 17,950$ for M2 where $f_{de} \\le -0.005$, and peaks around $z_{eq}$ with $f_{de} \\approx -0.019$ at the peak for M1 or $\\approx -0.012$ for M2 (inset). At late times, $f_{de}$ rises drastically and becomes at the present $f_{de}(z=0) \\approx 0.733$ for M1 or $\\approx 0.707$ for M2. Far in the future, it approaches $1$.","label":"RelContZ","source":"arxiv","key":"c2b9fd3608eff74b699eb8f93c409d00","url":"https://inspirehep.net/files/c2b9fd3608eff74b699eb8f93c409d00"},{"filename":"fig7.png","material":"preprint","caption":"Same as Fig.~\\ref{muVSzFull}; showing the prediction by the toy model ($\\al = 0.025$ and $\\Omega_{\\infty} h^2 = 0.4625$), see Appendix~\\ref{Toy_model}. The orange points at the bottom panel show the binned Pantheon data with $M_B = -19.346$, the best $M_B$ in terms of RMSD (\\EqRef{\\ref{RMSD_equation}}) for the Toy model.","label":"muVSzFullToyv6","source":"arxiv","key":"181875a850058abf0a033b787e0efb90","url":"https://inspirehep.net/files/181875a850058abf0a033b787e0efb90"},{"filename":"fig8.png","material":"preprint","caption":"Same as Fig.~\\ref{Eofzdata}; showing the prediction by the toy model ($\\al = 0.025$ and $\\Omega_{\\infty} h^2 = 0.4625$), see Appendix~\\ref{Toy_model}.","label":"EofzdataToyv6","source":"arxiv","key":"5cd4b5e9d48cf7e947a9189e80229e06","url":"https://inspirehep.net/files/5cd4b5e9d48cf7e947a9189e80229e06"},{"filename":"fig9.png","material":"preprint","caption":"Same as Fig.~\\ref{BAOdata}; showing the prediction by the toy model ($\\al = 0.025$ and $\\Omega_{\\infty} h^2 = 0.4625$), see Appendix~\\ref{Toy_model}.","label":"BAOdataToyv6","source":"arxiv","key":"95f711bc47ad08b9d7e46628144e9be4","url":"https://inspirehep.net/files/95f711bc47ad08b9d7e46628144e9be4"}],"legacy_version":"20210206061619.0","inspire_categories":[{"term":"Gravitation and Cosmology","source":"arxiv"},{"term":"Gravitation and Cosmology"}],"first_author":{"emails":["dror.berechya@weizmann.ac.il"],"full_name":"Berechya, Dror","last_name":"Berechya","first_name":"Dror","recid":1897202},"control_number":1811142,"dois":[{"source":"Oxford University Press","value":"10.1093/mnras/stab2345"},{"material":"publication","source":"arXiv","value":"10.1093/mnras/stab2345"}],"document_type":["article"],"texkeys":["Berechya:2020vcy","Leonhardt:2020qam"],"abstracts":[{"source":"Oxford University Press","value":"Dark energy is one of the greatest scientific mysteries of today. The idea that dark energy originates from quantum vacuum fluctuations has circulated since the late ’60s, but theoretical estimations of vacuum energy have disagreed with the measured value by many orders of magnitude, until recently. Lifshitz theory applied to cosmology has produced the correct order of magnitude for dark energy. Furthermore, the theory is based on well-established and experimentally well-tested grounds in atomic, molecular and optical physics. In this paper, we confront Lifshitz cosmology with astronomical data. We find that the dark–energy dynamics predicted by the theory is able to resolve the Hubble tension, the discrepancy between the observed and predicted Hubble constant within the standard cosmological model. The theory is consistent with supernovae data, Baryon Acoustic Oscillations and the Cosmic Microwave Background. Our findings indicate that Lifshitz cosmology is a serious candidate for explaining dark energy.","abstract_source_suggest":{"input":"Oxford University Press"}},{"source":"arXiv","value":"Dark energy is one of the greatest scientific mysteries of today. The idea that dark energy originates from quantum vacuum fluctuations has circulated since the late '60s, but theoretical estimations of vacuum energy have disagreed with the measured value by many orders of magnitude, until recently. Lifshitz theory applied to cosmology has produced the correct order of magnitude for dark energy. Furthermore, the theory is based on well-established and experimentally well-tested grounds in atomic, molecular and optical physics. In this paper, we confront Lifshitz cosmology with astronomical data. We find that the dark-energy dynamics predicted by the theory is able to resolve the Hubble tension, the discrepancy between the observed and predicted Hubble constant within the standard cosmological model. The theory is consistent with supernovae data, Baryon Acoustic Oscillations and the Cosmic Microwave Background. Our findings indicate that Lifshitz cosmology is a serious candidate for explaining dark energy.","abstract_source_suggest":{"input":"arXiv"}}],"primary_arxiv_category":["gr-qc"],"titles":[{"source":"Oxford University Press","title":"Lifshitz cosmology: quantum vacuum and Hubble tension"},{"source":"arXiv","title":"Lifshitz cosmology: quantum vacuum and Hubble tension"},{"source":"arXiv","title":"Hubble tension and quantum vacuum"},{"source":"arXiv","title":"Observed Hubble constant is consistent with physics of the quantum vacuum"}],"imprints":[{"date":"2021-09-14"}],"curated":true},"updated":"2024-04-09T12:29:28.293819+00:00","links":{"bibtex":"https://inspirehep.net/api/literature/1811142?format=bibtex","latex-eu":"https://inspirehep.net/api/literature/1811142?format=latex-eu","latex-us":"https://inspirehep.net/api/literature/1811142?format=latex-us","json":"https://inspirehep.net/api/literature/1811142?format=json","json-expanded":"https://inspirehep.net/api/literature/1811142?format=json-expanded","cv":"https://inspirehep.net/api/literature/1811142?format=cv","citations":"https://inspirehep.net/api/literature/?q=refersto%3Arecid%3A1811142"}},{"id":"1744525","created":"2019-07-19T00:00:00+00:00","metadata":{"citation_count":0,"publication_info":[{"journal_volume":"197","page_end":"314","conference_record":{"$ref":"https://inspirehep.net/api/conferences/1744343"},"year":2019,"journal_record":{"$ref":"https://inspirehep.net/api/journals/1212356"},"page_start":"309","journal_title":"Proc.Int.Sch.Phys.Fermi","parent_record":{"$ref":"https://inspirehep.net/api/literature/1744512"},"cnum":"C16-07-08.1"}],"authors":[{"full_name_unicode_normalized":"avni, yael","full_name":"Avni, Yael","record":{"$ref":"https://inspirehep.net/api/authors/2209740"},"ids":[{"schema":"INSPIRE BAI","value":"Y.Avni.1"}],"last_name":"Avni","signature_block":"AVNy","first_name":"Yael","uuid":"f42ad75f-5375-472b-863b-f64b0866f446","recid":2209740},{"full_name_unicode_normalized":"leonhardt, ulf","full_name":"Leonhardt, Ulf","record":{"$ref":"https://inspirehep.net/api/authors/1000555"},"ids":[{"schema":"INSPIRE BAI","value":"U.Leonhardt.1"}],"last_name":"Leonhardt","signature_block":"LANARDu","first_name":"Ulf","uuid":"b67b3f9f-7770-4ebe-9807-babec791c435","recid":1000555}],"citation_count_without_self_citations":0,"citeable":true,"$schema":"https://inspirehep.net/schemas/records/hep.json","number_of_pages":6,"legacy_version":"20190719231827.0","inspire_categories":[{"term":"General Physics"}],"legacy_creation_date":"2019-07-19","author_count":2,"first_author":{"full_name":"Avni, Yael","last_name":"Avni","first_name":"Yael","recid":2209740},"control_number":1744525,"dois":[{"source":"IOS Press","value":"10.3254/978-1-61499-937-9-309"}],"earliest_date":"2019","document_type":["conference paper"],"texkeys":["Avni:2019fjw"],"abstracts":[{"source":"IOS Press","value":"The most well-known manifestation of the Casimir effect is the attraction of two uncharged conducting plates. However, it turns out that Casimir forces are all around us: they originate from vacuum fluctuations of the electromagnetic field that excite dipoles in dielectric and conducting materials. These dipoles then interact with each other, generating measurable forces between macroscopic bodies: the Casimir force. A naive calculation of the Casimir force produces infinities, and though extensive work has been done in the field, there is still no universal prescription to renormalize the force. In this paper, we introduce the subject of Casimir forces and focus on the Casimir self-stress inside a homogeneous sphere. We discuss previous calculations and suggest an additional renormalization scheme that could solve the problem.","abstract_source_suggest":{"input":"IOS Press"}}],"titles":[{"source":"IOS Press","title":"Casimir forces in spherically symmetric dielectric media"}],"facet_author_name":["2209740_Y. Avni","1000555_Ulf Leonhardt"],"imprints":[{"date":"2019"}],"_oai":{"sets":["Literature"],"id":"oai:inspirehep.net:1744525","updated":"2023-03-06T15:20:44.811802"},"curated":false,"journal_title_variants":["Proc. Int. Sch. Phys. 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[4] in but it is still not clear what has caused the observation made in Ref. [3]"],"authors":[{"full_name":"Belgiorno, F."}]},"curated_relation":false,"record":{"$ref":"https://inspirehep.net/api/literature/882127"}},{"reference":{"label":"6","publication_info":{"journal_volume":"106","artid":"021302","year":2011,"journal_title":"Phys.Rev.Lett."},"misc":["Measurement of Stimulated Hawking Emission in an Analogue System"],"authors":[{"full_name":"Weinfurtner, S."},{"full_name":"Tedford, E.W."},{"full_name":"Penrice, M.C.J."},{"full_name":"Unruh, W.G."},{"full_name":"Lawrence, G.A."}]},"curated_relation":false,"record":{"$ref":"https://inspirehep.net/api/literature/864942"}},{"reference":{"label":"7","publication_info":{"journal_volume":"91","artid":"024020","year":2015,"journal_title":"Phys.Rev.D"},"misc":["Wave blocking and partial transmission in subcritical flows over an obstacle"],"authors":[{"full_name":"Euvé, L.-P."},{"full_name":"Michel, F."},{"full_name":"Parentani, R."},{"full_name":"Rousseaux, G."}]},"curated_relation":false,"record":{"$ref":"https://inspirehep.net/api/literature/1316328"}},{"reference":{"label":"8","publication_info":{"journal_volume":"10","artid":"864","year":2014,"page_start":"864","journal_title":"Nature Phys."},"misc":["Observation of self-amplifying Hawking radiation in an analogue black-hole laser, Nat. Phys. 10, 864"],"authors":[{"full_name":"Steinhauer, J."}]},"curated_relation":false,"record":{"$ref":"https://inspirehep.net/api/literature/1318645"},"legacy_curated":true},{"reference":{"label":"9","publication_info":{"journal_volume":"114","artid":"60011","year":2016,"journal_title":"EPL"},"misc":["Numerical study of a recent black-hole lasing experiment"],"authors":[{"full_name":"Tettamanti, M."},{"full_name":"Cacciatori, S.L."},{"full_name":"Parola, A."},{"full_name":"Carusotto, I."}]},"curated_relation":false,"record":{"$ref":"https://inspirehep.net/api/literature/1427709"}},{"reference":{"arxiv_eprint":"1605.01027","label":"10","misc":["Ch. W. Clark Mechanism of stimulated Hawking radiation in a laboratory BoseEinstein condensate"],"authors":[{"full_name":"Wang, Y.-H."},{"full_name":"Jacobson, T."},{"full_name":"Edwards, M."}]},"curated_relation":false,"record":{"$ref":"https://inspirehep.net/api/literature/1454394"}},{"reference":{"arxiv_eprint":"1608.02544","label":"11","misc":["Self-amplifying Hawking radiation and its background: a numerical study"],"authors":[{"full_name":"Steinhauer, J."},{"full_name":"de Nova, J.R.M."}]},"curated_relation":false,"record":{"$ref":"https://inspirehep.net/api/literature/1479942"}},{"reference":{"arxiv_eprint":"1605.09752","label":"12","misc":["Phonon spectrum and correlations in a transonic flow of an atomic Bose gas"],"authors":[{"full_name":"Michel, F."},{"full_name":"Coupechoux, J.-F."},{"full_name":"Parentani, R."}]},"curated_relation":false,"record":{"$ref":"https://inspirehep.net/api/literature/1466431"}},{"reference":{"label":"13","publication_info":{"journal_volume":"12","artid":"959","year":2016,"page_start":"959","journal_title":"Nature Phys."},"misc":["Observation of quantum Hawking radiation and its entanglement in an analogue black hole, Nat. Phys. 12, 959"],"authors":[{"full_name":"Steinhauer, J."}]},"curated_relation":false,"record":{"$ref":"https://inspirehep.net/api/literature/1395958"},"legacy_curated":true},{"reference":{"label":"14","publication_info":{"journal_volume":"15","artid":"1767","year":1998,"page_start":"1767","journal_title":"Class.Quant.Grav."},"misc":["Acoustic black holes: Horizons, ergospheres, and Hawking radiation"],"authors":[{"full_name":"Visser, M."}]},"curated_relation":false,"record":{"$ref":"https://inspirehep.net/api/literature/451722"}},{"reference":{"label":"15","publication_info":{"year":2003},"misc":["Bose-Einstein Condensation (Oxford Univ. Press,)"],"authors":[{"full_name":"Pitaevskii, L."},{"full_name":"Stringari, S."}]}},{"reference":{"label":"16","misc":["The scales ξin and ξout of the wavenumbers in the figures are related to each other by ξin/ξout = cout/cin, because ξ = /(mc0) [15]. In the experiment [13] cout = 0.57mm/s and cin = 0.25mm/s"]}},{"reference":{"label":"17","publication_info":{"journal_volume":"80","artid":"043601","year":2009,"journal_title":"Phys.Rev.A"},"misc":["Black-hole radiation in BoseEinstein condensates"],"authors":[{"full_name":"Macher, J."},{"full_name":"Parentani, R."}]},"curated_relation":false,"record":{"$ref":"https://inspirehep.net/api/literature/821229"}},{"reference":{"label":"18","publication_info":{"journal_volume":"80","artid":"043603","year":2009,"journal_title":"Phys.Rev.A"},"misc":["Bogoliubov theory of acoustic Hawking radiation in Bose-Einstein condensates"],"authors":[{"full_name":"Recati, A."},{"full_name":"Pavloff, N."},{"full_name":"Carusotto, I."}]},"curated_relation":false,"record":{"$ref":"https://inspirehep.net/api/literature/836127"}},{"reference":{"label":"19","publication_info":{"journal_volume":"87","artid":"124039","year":2013,"journal_title":"Phys.Rev.D"},"misc":["Dissipative fields in de Sitter and black hole spacetimes: Quantum entanglement due to pair production and dissipation"],"authors":[{"full_name":"Adamek, J."},{"full_name":"Busch, X."},{"full_name":"Parentani, R."}]},"curated_relation":false,"record":{"$ref":"https://inspirehep.net/api/literature/1210642"}},{"reference":{"label":"20","misc":["The section on measuring the population of Hawking radiation in the article [13] mentions a correction factor of 2.2 for the population outside the horizon and a factor of 2.3 for the population inside, which indicates that the population nP was measured and not only nH"]}},{"reference":{"label":"21","misc":["The convolution of the Planck curve (1) as function of ω(kin) with a Gaussian would diverge due to the pole (5) unless it is cut off"]}},{"reference":{"label":"21","misc":["here we cut it off for kinξin < 0.05"]}},{"reference":{"label":"22","misc":["The article [13] does not contain sufficient information for an accurate description of the component of σ that is solely due to the finite time of the experiment. In this paper a conservative ad-hoc model is used (inset of Fig. 4): between kpeak and the data point next below in Fig. 1a σ rises linearly from zero to the error bar of kpeak. This is an overestimation"]}},{"reference":{"label":"22","misc":["the actual σ will be smaller, and so the actual deviation of n(n + 1) (Fig. 4b, dotted red curve) from the one of the article [13] (Fig. 4b, solid red curve) will be even stronger"]}},{"reference":{"label":"23","publication_info":{"journal_volume":"92","artid":"024043","year":2015,"journal_title":"Phys.Rev.D"},"misc":["Measuring the entanglement of analogue Hawking radiation by the density-density correlation function"],"authors":[{"full_name":"Steinhauer, J."}]},"curated_relation":false,"record":{"$ref":"https://inspirehep.net/api/literature/1364714"}},{"reference":{"label":"24","publication_info":{"journal_volume":"117","artid":"121301","year":2016,"journal_title":"Phys.Rev.Lett."},"misc":["Observation of noise correlated by the Hawking effect in a water tank"],"authors":[{"full_name":"Euvé, L.-P."},{"full_name":"Michel, F."},{"full_name":"Parentani, R."},{"full_name":"Philbin, T.G."},{"full_name":"Rousseaux, G."}]},"curated_relation":false,"record":{"$ref":"https://inspirehep.net/api/literature/1406548"}},{"reference":{"label":"25","publication_info":{"year":2010},"misc":["Essential Quantum Optics: From Quantum Measurements to Black Holes, (Cambridge University Press, Cambridge,)"],"authors":[{"full_name":"Leonhardt, U."}]}},{"reference":{"label":"26","misc":["The process of Hawking radiation [25] transforms the initial annihilation operators â1 and â2 into ˆbH = â1 cosh ζ + ↠2 sinh ζ and ˆbP = â2 cosh ζ + ↠1 sinh ζ with tanh2 ζ = exp(- ω/KT). Suppose the initial state is |α 1|0 2 with |α being a coherent state [25]. One finds that the final state is always entangled. However, in the article [13], it would only appear to be entangled for |α|2 < exp(- ω/KT), as only then the correlation exceeds n2 that nH = nP here, which would still be consistent with the published data [13]"],"authors":[{"full_name":"Note, H."}]}},{"reference":{"label":"27","publication_info":{"journal_volume":"536","artid":"133","year":2016,"page_start":"133","journal_title":"Nature"},"misc":["Hopes for revolutionary new LHC particle dashed"],"authors":[{"full_name":"Gibney, E."}]}}],"number_of_pages":6,"legacy_creation_date":"2016-09-14","preprint_date":"2016-09-13","author_count":1,"public_notes":[{"source":"arXiv","value":"Accepted by Annalen der Physik 5 September 2017; published electronically 26 March 2018 https://doi.org/10.1002/andp.201700114"}],"earliest_date":"2016-09-13","refereed":true,"external_system_identifiers":[{"schema":"MSNET","value":"3808129"}],"facet_author_name":["1000555_Ulf Leonhardt"],"core":true,"license":[{"imposing":"arXiv","url":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/"}],"_oai":{"sets":["Literature"],"id":"oai:inspirehep.net:1486379","updated":"2023-10-03T08:21:53.312454"},"journal_title_variants":["Annalen Phys."],"arxiv_eprints":[{"categories":["gr-qc"],"value":"1609.03803"}],"referenced_authors_bais":["C.W.Clark.1","R.Sch.tzhold.2","L.P.Euve.1","M.Edwards.3","V.G.Sala.2","F.Belgiorno.1","E.W.Tedford.2","M.C.J.Penrice.2","Julian.Adamek.1","F.Michel.1","J.F.Coupechoux.1","M.Tettamanti.1","J.Steinhauer.1","Stephen.W.Hawking.1","T.A.Jacobson.1","S.L.Cacciatori.1","Silke.Weinfurtner.1","J.Macher.2","E.Rubino.2","G.Ortenzi.2","Daniele.Faccio.1","Y.H.Wang.4","R.Parentani.1","G.Rousseaux.2","X.Busch.1","Juan.Ramon.Munoz.de.Nova.1","V.Gorini.1","Matt.Visser.1","A.Recati.2","L.Rizzi.2","G.A.Lawrence.2","M.Clerici.2","A.Parola.2","N.Pavloff.1","I.Carusotto.1","T.G.Philbin.4","W.G.Unruh.1"],"figures":[{"filename":"fig1.png","caption":"\\small{ Dispersion measurements. {\\bf a} inside the horizon: wavenumbers $k_\\mathrm{in}$ corresponding to frequencies in units with $\\hbar\\omega_\\mathrm{in} = mc_\\mathrm{in}^2$ where $m$ is the atomic mass; $\\xi_\\mathrm{in}$ is the dispersion/healing length of Eq.~(\\ref{bogoliubov}). The gray curves show the solutions of the dispersion relation, Eq.~(\\ref{dispersion}), with fitted parameters. One sees two branches, one (full dots) of Hawking waves trying to escape but not succeeding, the other (open dots when distinguishable) of waves propagating with the flow. At $k_\\mathrm{peak}$ the Hawking waves are fast enough to reach the flow velocity and are no longer trapped; there is no horizon beyond the critical frequency $\\omega_c$. {\\bf b} outside the horizon: wavenumbers \\cite{Scaling} versus frequencies (notation analogous to {\\bf a}). Here $k_\\mathrm{c}$ is the wavenumber that corresponds to $\\omega_c$. The data points and error bars were taken from Fig.~3 of the article \\cite{Steinhauer}. { Note that the error bars correspond to the half width at half maximum of the observed resolution \\cite{Steinhauer}; one has to divide them by $1.2$ for getting the standard deviation $\\sigma$ \\cite{SteinhauerReply}.} }","source":"arxiv","key":"397f244422f58fc4745d734338708b66","url":"https://inspirehep.net/files/397f244422f58fc4745d734338708b66"},{"filename":"fig2.png","caption":"\\small{ Population of outgoing particles. The blue dots represent the phonon populations $\\overline{n}$ obtained from experiment \\cite{Steinhauer} at wavenumbers $k_\\mathrm{out}$ outside the horizon (notation as in Fig.~\\ref{stein3}). The points are surrounded by their vertical error bars; the dark--blue area represents $1\\sigma$ and the light--blue area $2\\sigma$ (where $\\sigma$ means the standard deviation). The data were taken from Fig.~5b of the article \\cite{Steinhauer}. The population is zero within the error bars for the data points corresponding to frequencies beyond $\\omega_\\mathrm{c}$ (Fig.~\\ref{stein3}). The red line shows a fit with a Planck curve linearly brought to zero at $\\omega_\\mathrm{c}$, as the insert illustrates. There the dotted line is the Planck curve continued beyond the red point of deviation. The data is consistent with the dispersion measurements (Fig.~\\ref{stein3}) and theoretical expectations, but the spectrum is clearly not Planckian. }","source":"arxiv","key":"63601100b0b0af323710784b529be056","url":"https://inspirehep.net/files/63601100b0b0af323710784b529be056"},{"filename":"fig3.png","caption":"\\small{ Entanglement. The Hawking phonons are entangled with their partners if the correlations $|\\langle \\hat{b}_\\mathrm{H}\\hat{b}_\\mathrm{P}\\rangle|^2$ (black dots) lie above the populations squared $\\overline{n}^2$ (blue dots), assuming the populations of Hawking and partner particles are the same. As in Fig.~\\ref{stein5} the points are surrounded by their vertical error bars; the darker areas indicate $1\\sigma$, the lighter areas $2\\sigma$. The data (from Fig.~6a of Ref.~\\cite{Steinhauer} without $S_0^2$ prefactor \\cite{S0}) are shown versus wavenumber $k_\\mathrm{in}$ inside the horizon; the $k_\\mathrm{out}$ of the populations (Fig.~\\ref{stein5}) are transformed via $\\omega$ into $k_\\mathrm{in}$ (Fig.~\\ref{stein3}). The populations vanish beyond $k_\\mathrm{peak}$ (red dot) but not the correlations. The red curve shows the Heisenberg limit $\\overline{n}(\\overline{n}+1)$ with $\\overline{n}$ obtained by convoluting the population curve with a Gaussian (Fig.~\\ref{convolution}). }","source":"arxiv","key":"dd063326783bea34a352fd789f7c583b","url":"https://inspirehep.net/files/dd063326783bea34a352fd789f7c583b"},{"filename":"fig4.png","caption":"\\small{ Convolution. {\\bf a}: The fitted population curve (dark blue, from Fig.~\\ref{stein5}) is represented as function of $k_\\mathrm{in}\\xi_\\mathrm{in}$ and convoluted with a Gaussian to produce the red curve for $\\overline{n}$ that gives the Heisenberg limit $\\overline{n}(\\overline{n}+1)$ of Fig.~\\ref{stein6} in agreement with the article \\cite{Steinhauer}. The standard deviation of the Gaussian was set to the constant $1.21$. The dotted curve shows the population curve convoluted with variable standard deviation $\\sigma$ displayed in the insert that reflects the actual uncertainty in $k_\\mathrm{in}\\xi_\\mathrm{in}$ taken from the dispersion measurements \\cite{Remark} (Fig.~\\ref{stein3}). {\\bf b}: comparison of the Heisenberg limits $\\overline{n}(\\overline{n}+1)$ with fixed (red) and variable (red, dotted) convolution with the particle correlations \\cite{Steinhauer} (black dots with uncertainty regions from Fig.~\\ref{stein6}). Beyond the critical wavenumber $k_\\mathrm{peak}$ the correlation curve tends to lie above the corrected Heisenberg limit (dotted line), which violates the fundamental bounds of Eq.~(\\ref{bounds}). }","source":"arxiv","key":"14dfc7b57836b8e68491f6c019915417","url":"https://inspirehep.net/files/14dfc7b57836b8e68491f6c019915417"},{"filename":"fig5a.png","caption":"\\small{ Entanglement with full error bars. The data of Fig.~\\ref{stein6} is shown with full error regions (ellipses). The uncertainties in the variables $k_\\mathrm{in}\\xi_\\mathrm{in}$ are obtained from Eq.~(\\ref{sigma}) and the dispersion measurements (Fig.~\\ref{stein3}) \\cite{Scaling}. $\\bm{1\\sigma}$: the correlations $|\\langle \\hat{b}_\\mathrm{H}\\hat{b}_\\mathrm{P}\\rangle|^2$ (black dots, gray ellipses) are distinguishable from the populations squared $\\overline{n}^2$ (blue dots, lightblue ellipses). $\\bm{2\\sigma}$: the curves are indistinguishable. }","source":"arxiv","key":"9d87b2be13c22029cc2506facf2e8121","url":"https://inspirehep.net/files/9d87b2be13c22029cc2506facf2e8121"},{"filename":"fig5b.png","caption":"\\small{ Entanglement with full error bars. The data of Fig.~\\ref{stein6} is shown with full error regions (ellipses). The uncertainties in the variables $k_\\mathrm{in}\\xi_\\mathrm{in}$ are obtained from Eq.~(\\ref{sigma}) and the dispersion measurements (Fig.~\\ref{stein3}) \\cite{Scaling}. $\\bm{1\\sigma}$: the correlations $|\\langle \\hat{b}_\\mathrm{H}\\hat{b}_\\mathrm{P}\\rangle|^2$ (black dots, gray ellipses) are distinguishable from the populations squared $\\overline{n}^2$ (blue dots, lightblue ellipses). $\\bm{2\\sigma}$: the curves are indistinguishable. }","source":"arxiv","key":"2b5a25d29583d7501d899d6831b59465","url":"https://inspirehep.net/files/2b5a25d29583d7501d899d6831b59465"}],"legacy_version":"20190409162455.0","inspire_categories":[{"term":"Gravitation and Cosmology"}],"first_author":{"affiliations_identifiers":[{"schema":"ROR","value":"https://ror.org/0316ej306"}],"full_name":"Leonhardt, Ulf","last_name":"Leonhardt","first_name":"Ulf","recid":1000555},"control_number":1486379,"dois":[{"value":"10.1002/andp.201700114"}],"document_type":["article"],"texkeys":["Leonhardt:2016qdi"],"abstracts":[{"source":"WILEY","value":"A recent article [J. 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When there are two horizons, however, Corley and Jacobson have shown that superluminal dispersion leads to an amplification of the particle production in the case of bosons. The analytic theory of this 'black hole laser' process is quite complicated, so we provide some numerical results in the hope of aiding understanding of this interesting phenomenon. Specifically, we consider sonic horizons in a moving fluid. The theory of elementary excitations in a Bose-Einstein condensate provides an example of 'superluminal' (Bogoliubov) dispersion, so we add Bogoliubov dispersion to Unruh's equation for sound in the fluid. A white-hole/black-hole horizon pair will then display black hole lasing. Numerical analysis of the evolution of a wave packet gives a clear picture of the amplification process. 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