Semiclassical theory of out-of-time-order correlators for low-dimensional classically chaotic systems - INSPIRE

DataBETA

Semiclassical theory of out-of-time-order correlators for low-dimensional classically chaotic systems

Rodolfo A. Jalabert
(
- IPCMS, Strasbourg
)
,
Ignacio García-Mata
(
- IFIMAR, Buenos Aires and
- Buenos Aires, CONICET
)
,
Diego A. Wisniacki
(
- Buenos Aires U.
)

Aug 13, 2018

12 pages

Published in:

Phys.Rev.E 98 (2018) 6, 062218

Published: Dec 22, 2018

e-Print:

1808.04383 [quant-ph]

DOI:

10.1103/PhysRevE.98.062218

View in:

reference search64 citations

Citations per year

Abstract: (APS)

The out-of-time-order correlator (OTOC), recently analyzed in several physical contexts, is studied for low-dimensional chaotic systems through semiclassical expansions and numerical simulations. The semiclassical expansion for the OTOC yields a leading-order contribution in ℏ2 that is exponentially increasing with time within an intermediate, temperature-dependent, time window. The growth-rate in such a regime is governed by the Lyapunov exponent of the underlying classical system and scales with the square-root of the temperature.

Note:

24 pages (one column), 7 figures. Some changes and corrections added. Closest to published version

Nonlinear Dynamics and Chaos

References(46)

Figures(7)

[1]

Unscrambling the physics of out-of-time-order correlators

Brian Swingle
(
- Joint Quantum Inst., College Park and
- Santa Barbara, KITP
)

- Nature Phys. 14 (2018) 10, 988-990
•
DOI:
- 10.1038/s41567-018-0295-5

[2]

A. Larkin
,
Y.N. Ovchinnikov

- Zh.Eksp.Teor.Fiz.Sov.Phys. 55 (1968) 1200

[2]

A. Larkin
,
Y.N. Ovchinnikov

- Sov.Phys.JETP 28 (1969) 1200

[3]

A bound on chaos

- JHEP 08 (2016) 106
•
e-Print:
- 1503.01409
•
DOI:
- 10.1007/JHEP08(2016)106

[4]

Measuring the scrambling of quantum information

Brian Swingle
(
- Stanford U., Phys. Dept. and
- Stanford U., ITP
)
,
Gregory Bentsen
(
- Stanford U., Phys. Dept.
)
,
Monika Schleier-Smith
(
- Stanford U., Phys. Dept.
)
,
Patrick Hayden
(
- Stanford U., Phys. Dept. and
- McGill U. and
- Stanford U., ITP
)

- Phys.Rev.A 94 (2016) 4, 040302
•
e-Print:
- 1602.06271
•
DOI:
- 10.1103/PhysRevA.94.040302

[5]

Microscopic model of quantum butterfly effect: out-of-time-order correlators and traveling combustion waves

Igor L. Aleiner
(
- Columbia U.
)
,
Lara Faoro
(
- Paris, LPTHE and
- Rutgers U., Piscataway
)
,
Lev B. Ioffe
(
- Paris, LPTHE and
- Rutgers U., Piscataway
)

- Annals Phys. 375 (2016) 378-406
•
e-Print:
- 1609.01251
•
DOI:
- 10.1016/j.aop.2016.09.006

[6]

Thermodynamics of quantum information scrambling

Michele Campisi
(
- NEST-INFM
)
,
John Goold
(
- ICTP, Trieste
)

- Phys.Rev.E 95 (2017) 6, 062127
•
e-Print:
- 1609.05848
•
DOI:
- 10.1103/PhysRevE.95.062127

[7]

Weak Quantum Chaos

- Phys.Rev.B 96 (2017) 6, 060301
•
e-Print:
- 1701.09147
•
DOI:
- 10.1103/PhysRevB.96.060301

[8]

Lyapunov Exponent and Out-of-Time-Ordered Correlator’s Growth Rate in a Chaotic System

Efim B. Rozenbaum
(
- Maryland U. and
- Nordita and
- Royal Inst. Tech., Stockholm
)
,
Sriram Ganeshan
(
- Stony Brook U., New York, SCGP and
- Maryland U. and
- Nordita and
- Royal Inst. Tech., Stockholm
)
,
Victor Galitski
(
- Maryland U. and
- Nordita and
- Royal Inst. Tech., Stockholm and
- Monash U.
)

- Phys.Rev.Lett. 118 (2017) 8, 086801
•
e-Print:
- 1609.01707
•
DOI:
- 10.1103/PhysRevLett.118.086801

[9]

Out-of-time-order correlators in quantum mechanics

- JHEP 10 (2017) 138
•
e-Print:
- 1703.09435
•
DOI:
- 10.1007/JHEP10(2017)138

[10]

Measuring Out-of-Time-Order Correlators on a Nuclear Magnetic Resonance Quantum Simulator

et al.

- Phys.Rev.X 7 (2017) 3, 031011
•
e-Print:
- 1609.01246
•
DOI:
- 10.1103/PhysRevX.7.031011

[11]

Out-of-time-order Operators and the Butterfly Effect

Jordan S. Cotler
(
- Stanford U., ITP
)
,
Dawei Ding
(
- Stanford U., ITP
)
,
Geoffrey R. Penington
(
- Stanford U., ITP
)

- Annals Phys. 396 (2018) 318-333,
- Annals of Physics, Volume 396, 2018, Pages 318-333
•
e-Print:
- 1704.02979
•
DOI:
- 10.1016/j.aop.2018.07.020

[12]

Measuring out-of-time-order correlations and multiple quantum spectra in a trapped ion quantum magnet

Martin Gärttner
(
- JILA, Boulder and
- U. Colorado, Boulder
)
,
Justin G. Bohnet
(
- NIST, Boulder
)
,
Arghavan Safavi-Naini
(
- JILA, Boulder and
- U. Colorado, Boulder
)
,
Michael L. Wall
(
- JILA, Boulder and
- U. Colorado, Boulder
)
,
John J. Bollinger
(
- NIST, Boulder
)

et al.

- Nature Phys. 13 (2017) 781
•
e-Print:
- 1608.08938
•
DOI:
- 10.1038/nphys4119

[13]

J. Kurchan

- J.Statist.Phys. 171 (2018) 965
•
DOI:
- 10.1007/s10955-018-2052-7

[14]

Universal level statistics of the out-of-time-ordered operator

- Phys.Rev.B 100 (2019) 3, 035112
•
e-Print:
- 1801.10591
•
DOI:
- 10.1103/PhysRevB.100.035112

[15]

Operator scrambling and quantum chaos

Xiao Chen
(
- Santa Barbara, KITP
)
,
Tianci Zhou
(
- Illinois U., Urbana
)

e-Print:
- 1804.08655

[16]

Many-Body Quantum Interference and the Saturation of Out-of-Time-Order Correlators

- Phys.Rev.Lett. 121 (2018) 12, 124101
•
e-Print:
- 1805.06377
•
DOI:
- 10.1103/PhysRevLett.121.124101

[17]

Chaos signatures in the short and long time behavior of the out-of-time ordered correlator

Ignacio García-Mata
(
- IFIMAR, Buenos Aires and
- Buenos Aires, CONICET
)
,
Marcos Saraceno
(
- CNEA, Buenos Aires and
- San Martin Natl. U.
)
,
Rodolfo A. Jalabert
(
- IPCMS, Strasbourg
)
,
Augusto J. Roncaglia
(
- Buenos Aires U.
)
,
Diego A. Wisniacki
(
- Buenos Aires U.
)

- Phys.Rev.Lett. 121 (2018) 21, 210601
•
e-Print:
- 1806.04281
•
DOI:
- 10.1103/PhysRevLett.121.210601

[18]

R. Hamazaki
,
K. Fujimoto
,
M. Ueda

e-Print:
- 1807.02360

[19]

Quantum and Classical Lyapunov Exponents in Atom-Field Interaction Systems

Jorge Chávez-Carlos
(
- Mexico U., ICN
)
,
B. López-Del-Carpio
(
- Mexico U., ICN
)
,
Miguel A. Bastarrachea-Magnani
(
- Freiburg U.
)
,
Pavel Stránský
(
- Charles U.
)
,
Sergio Lerma-Hernández
(
- Veracruz U.
)

et al.

- Phys.Rev.Lett. 122 (2019) 2, 024101
•
e-Print:
- 1807.10292
•
DOI:
- 10.1103/PhysRevLett.122.024101

[20]

Characterization of chaotic quantum spectra and universality of level fluctuation laws

- Phys.Rev.Lett. 52 (1984) 1-4
•
DOI:
- 10.1103/PhysRevLett.52.1

[21]

D. Ullmo

- Scholarpedia 11 (2016) 31721
•
DOI:
- 10.4249/scholarpedia.31721

[22]

Chaos and Quantum Physics

M.-J. Giannoni
,
A. Voros
,
J. Zinn-Justin

[23]

Chaos in Classical and Quantum Mechanics

M.C. Gutzwiller

[24]

Environment-Independent Decoherence Rate in Classically Chaotic Systems

- Phys.Rev.Lett. 86 (2001) 12, 2490
•
DOI:
- 10.1103/PhysRevLett.86.2490

1-25 of 46
1
2
25 / page