Thermodynamics of photons on fractals
Oct, 20105 pages
Published in:
- Phys.Rev.Lett. 105 (2010) 230407
e-Print:
- 1010.1148 [cond-mat.stat-mech]
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Abstract: (arXiv)
A thermodynamical treatment of a massless scalar field (a 'photon') confined to a fractal spatial manifold leads to an equation of state relating pressure to internal energy, , where is the spectral dimension and defines the 'spectral volume'. For regular manifolds, coincides with the usual geometric spatial volume, but on a fractal this is not necessarily the case. This is further evidence that on a fractal, momentum space can have a different dimension than position space. Our analysis also provides a natural definition of the vacuum (Casimir) energy of a fractal. We suggest ways that these unusual properties might be probed experimentally.- 11.10.Kk
- 04.62.+v
- 05.30.-d
- field theory: scalar: massless
- fractal
- dimension: spectral
- photon
- thermodynamics
- vacuum state: energy
- geometry
References(28)
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