Work Statistics, Loschmidt Echo and Information Scrambling in Chaotic Quantum Systems
Abstract
Characterizing the work statistics of driven complex quantum systems is generally challenging because of the exponential growth with the system size of the number of transitions involved between different energy levels. We consider the quantum work distribution associated with the driving of chaotic quantum systems described by random matrix Hamiltonians and characterize exactly the work statistics associated with a sudden quench for arbitrary temperature and system size. Knowledge of the work statistics yields the Loschmidt echo dynamics of an entangled state between two copies of the system of interest, the thermofield double state. This echo dynamics is dictated by the spectral form factor. We discuss its relation to frame potentials and its use to assess information scrambling.
- Authors:
-
[1];
[2];
[3]
- Donostia International Physics Center, San Sebastian (Spain); IKERBASQUE, Bilbao (Spain); Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
- Technical Univ. of Cartagena, Cartagena (Spain)
- Donostia International Physics Center, San Sebastian (Spain); IKERBASQUE, Bilbao (Spain); Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Univ. of Massachusetts, Boston, MA (United States)
- Publication Date:
- Research Org.:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1525836
- Report Number(s):
- LA-UR-18-23369
Journal ID: ISSN 2521-327X
- Grant/Contract Number:
- 89233218CNA000001
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Quantum
- Additional Journal Information:
- Journal Volume: 3; Journal ID: ISSN 2521-327X
- Publisher:
- Quantum Science Open Community
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Quantum chaotic systems
Citation Formats
Chenu, Aurélia, Molina-Vilaplana, Javier, and del Campo, Adolfo. Work Statistics, Loschmidt Echo and Information Scrambling in Chaotic Quantum Systems. United States: N. p., 2019.
Web. doi:10.22331/q-2019-03-04-127.
Chenu, Aurélia, Molina-Vilaplana, Javier, & del Campo, Adolfo. Work Statistics, Loschmidt Echo and Information Scrambling in Chaotic Quantum Systems. United States. https://doi.org/10.22331/q-2019-03-04-127
Chenu, Aurélia, Molina-Vilaplana, Javier, and del Campo, Adolfo. Mon .
"Work Statistics, Loschmidt Echo and Information Scrambling in Chaotic Quantum Systems". United States. https://doi.org/10.22331/q-2019-03-04-127. https://www.osti.gov/servlets/purl/1525836.
@article{osti_1525836,
title = {Work Statistics, Loschmidt Echo and Information Scrambling in Chaotic Quantum Systems},
author = {Chenu, Aurélia and Molina-Vilaplana, Javier and del Campo, Adolfo},
abstractNote = {Characterizing the work statistics of driven complex quantum systems is generally challenging because of the exponential growth with the system size of the number of transitions involved between different energy levels. We consider the quantum work distribution associated with the driving of chaotic quantum systems described by random matrix Hamiltonians and characterize exactly the work statistics associated with a sudden quench for arbitrary temperature and system size. Knowledge of the work statistics yields the Loschmidt echo dynamics of an entangled state between two copies of the system of interest, the thermofield double state. This echo dynamics is dictated by the spectral form factor. We discuss its relation to frame potentials and its use to assess information scrambling.},
doi = {10.22331/q-2019-03-04-127},
journal = {Quantum},
number = ,
volume = 3,
place = {United States},
year = {Mon Mar 04 00:00:00 EST 2019},
month = {Mon Mar 04 00:00:00 EST 2019}
}
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Figure 1: Characteristic function of the work pdf for a sudden quench between two GUE Hamiltonians. 〈$χ$($t, τ$)〉 from the analytical solution (solid line, Eq. 18), and as obtained numerically averaging over 50000 realizations of the GUE at infinite temperature (red) and $β$ = 1 (blue). The numerical solutions convergemore »
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Works referenced in this record:
Onset of chaos and its signature in the spectral autocorrelation function
journal, February 1993
- Alhassid, Y.; Whelan, N.
- Physical Review Letters, Vol. 70, Issue 5
Black holes as mirrors: quantum information in random subsystems
journal, September 2007
- Hayden, Patrick; Preskill, John
- Journal of High Energy Physics, Vol. 2007, Issue 09
Computational complexity and black hole horizons: Computational complexity and black hole horizons
journal, January 2016
- Susskind, Leonard
- Fortschritte der Physik, Vol. 64, Issue 1
Universal Work Fluctuations During Shortcuts to Adiabaticity by Counterdiabatic Driving
journal, March 2017
- Funo, Ken; Zhang, Jing-Ning; Chatou, Cyril
- Physical Review Letters, Vol. 118, Issue 10
On long time unitarity restoring processes in the presence of eternal black holes
journal, June 2004
- Barbón, J. L. F.; Rabinovici, E.
- Fortschritte der Physik, Vol. 52, Issue 67
Eternal black holes in anti-de Sitter
journal, April 2003
- Maldacena, Juan
- Journal of High Energy Physics, Vol. 2003, Issue 04
Chaos and complexity by design
journal, April 2017
- Roberts, Daniel A.; Yoshida, Beni
- Journal of High Energy Physics, Vol. 2017, Issue 4
Digital Quantum Simulation of Spin Models with Circuit Quantum Electrodynamics
journal, June 2015
- Salathé, Y.; Mondal, M.; Oppliger, M.
- Physical Review X, Vol. 5, Issue 2
Integration with Respect to the Haar Measure on Unitary, Orthogonal and Symplectic Group
journal, March 2006
- Collins, Benoît; Śniady, Piotr
- Communications in Mathematical Physics, Vol. 264, Issue 3
Log-Gases and Random Matrices (LMS-34)
book, December 2010
- Forrester, Peter J.
- London Mathematical Society Monographs, Vol. 34
Chaos, complexity, and random matrices
journal, November 2017
- Cotler, Jordan; Hunter-Jones, Nicholas; Liu, Junyu
- Journal of High Energy Physics, Vol. 2017, Issue 11
Quantum statistics and the performance of engine cycles
journal, July 2015
- Zheng, Yuanjian; Poletti, Dario
- Physical Review E, Vol. 92, Issue 1
Work distributions for random sudden quantum quenches
journal, May 2017
- Łobejko, Marcin; Łuczka, Jerzy; Talkner, Peter
- Physical Review E, Vol. 95, Issue 5
Quantum simulation
journal, March 2014
- Georgescu, I. M.; Ashhab, S.; Nori, Franco
- Reviews of Modern Physics, Vol. 86, Issue 1
Experimental test of the quantum Jarzynski equality with a trapped-ion system
journal, December 2014
- An, Shuoming; Zhang, Jing-Ning; Um, Mark
- Nature Physics, Vol. 11, Issue 2
Quantum work statistics, Loschmidt echo and information scrambling
journal, August 2018
- Chenu, A.; Egusquiza, I. L.; Molina-Vilaplana, J.
- Scientific Reports, Vol. 8, Issue 1
Fast scramblers
journal, October 2008
- Sekino, Yasuhiro; Susskind, L.
- Journal of High Energy Physics, Vol. 2008, Issue 10
Irreversible Work and Inner Friction in Quantum Thermodynamic Processes
journal, December 2014
- Plastina, F.; Alecce, A.; Apollaro, T. J. G.
- Physical Review Letters, Vol. 113, Issue 26
Nonequilibrium Equality for Free Energy Differences
journal, April 1997
- Jarzynski, C.
- Physical Review Letters, Vol. 78, Issue 14
Jarzynski-like equality for the out-of-time-ordered correlator
journal, January 2017
- Yunger Halpern, Nicole
- Physical Review A, Vol. 95, Issue 1
Asymptotic behavior of group integrals in the limit of infinite rank
journal, May 1978
- Weingarten, Don
- Journal of Mathematical Physics, Vol. 19, Issue 5
Using a quantum work meter to test non-equilibrium fluctuation theorems
journal, November 2017
- Cerisola, Federico; Margalit, Yair; Machluf, Shimon
- Nature Communications, Vol. 8, Issue 1
Generalized Clausius Inequality for Nonequilibrium Quantum Processes
journal, October 2010
- Deffner, Sebastian; Lutz, Eric
- Physical Review Letters, Vol. 105, Issue 17
Environment-Independent Decoherence Rate in Classically Chaotic Systems
journal, March 2001
- Jalabert, Rodolfo A.; Pastawski, Horacio M.
- Physical Review Letters, Vol. 86, Issue 12
The role of quantum information in thermodynamics—a topical review
journal, February 2016
- Goold, John; Huber, Marcus; Riera, Arnau
- Journal of Physics A: Mathematical and Theoretical, Vol. 49, Issue 14
Digital Quantum Simulation of Minimal
journal, July 2017
- García-Álvarez, L.; Egusquiza, I. L.; Lamata, L.
- Physical Review Letters, Vol. 119, Issue 4
Quantum thermodynamics
journal, July 2016
- Vinjanampathy, Sai; Anders, Janet
- Contemporary Physics, Vol. 57, Issue 4
Measuring out-of-time-order correlations and multiple quantum spectra in a trapped-ion quantum magnet
journal, May 2017
- Gärttner, Martin; Bohnet, Justin G.; Safavi-Naini, Arghavan
- Nature Physics, Vol. 13, Issue 8
Digitized adiabatic quantum computing with a superconducting circuit
journal, June 2016
- Barends, R.; Shabani, A.; Lamata, L.
- Nature, Vol. 534, Issue 7606
Colloquium : Quantum fluctuation relations: Foundations and applications
journal, July 2011
- Campisi, Michele; Hänggi, Peter; Talkner, Peter
- Reviews of Modern Physics, Vol. 83, Issue 3
Work Measurement as a Generalized Quantum Measurement
journal, December 2014
- Roncaglia, Augusto J.; Cerisola, Federico; Paz, Juan Pablo
- Physical Review Letters, Vol. 113, Issue 25
Correlation Hole of Survival Probability and Level Statistics
journal, November 1995
- Ma, Jian-Zhong
- Journal of the Physical Society of Japan, Vol. 64, Issue 11
Black holes and random matrices
journal, May 2017
- Cotler, Jordan S.; Gur-Ari, Guy; Hanada, Masanori
- Journal of High Energy Physics, Vol. 2017, Issue 5
Quantum work for sudden quenches in Gaussian random Hamiltonians
journal, July 2018
- Arrais, Eric G.; Wisniacki, Diego A.; Céleri, Lucas C.
- Physical Review E, Vol. 98, Issue 1
Universal Digital Quantum Simulation with Trapped Ions
journal, September 2011
- Lanyon, B. P.; Hempel, C.; Nigg, D.
- Science, Vol. 334, Issue 6052
2D CFT partition functions at late times
journal, August 2017
- Dyer, Ethan; Gur-Ari, Guy
- Journal of High Energy Physics, Vol. 2017, Issue 8
Local Operators in the Eternal Black Hole
journal, November 2015
- Papadodimas, Kyriakos; Raju, Suvrat
- Physical Review Letters, Vol. 115, Issue 21
Fourier Transform: A Tool to Measure Statistical Level Properties in Very Complex Spectra
journal, June 1986
- Leviandier, Luc; Lombardi, Maurice; Jost, Rémi
- Physical Review Letters, Vol. 56, Issue 23
Driven Quantum Dynamics: Will It Blend?
journal, October 2017
- Banchi, Leonardo; Burgarth, Daniel; Kastoryano, Michael J.
- Physical Review X, Vol. 7, Issue 4
Quantum Szilard Engine with Attractively Interacting Bosons
journal, March 2018
- Bengtsson, J.; Tengstrand, M. Nilsson; Wacker, A.
- Physical Review Letters, Vol. 120, Issue 10
A bound on chaos
journal, August 2016
- Maldacena, Juan; Shenker, Stephen H.; Stanford, Douglas
- Journal of High Energy Physics, Vol. 2016, Issue 8
Butterflies from information metric
journal, September 2016
- Miyaji, Masamichi
- Journal of High Energy Physics, Vol. 2016, Issue 9
Experimental Reconstruction of Work Distribution and Study of Fluctuation Relations in a Closed Quantum System
journal, October 2014
- Batalhão, Tiago B.; Souza, Alexandre M.; Mazzola, Laura
- Physical Review Letters, Vol. 113, Issue 14
Cool horizons for entangled black holes
journal, August 2013
- Maldacena, J.; Susskind, L.
- Fortschritte der Physik, Vol. 61, Issue 9
Measuring Out-of-Time-Order Correlators on a Nuclear Magnetic Resonance Quantum Simulator
journal, July 2017
- Li, Jun; Fan, Ruihua; Wang, Hengyan
- Physical Review X, Vol. 7, Issue 3
Semiclassical approach to the work distribution
journal, November 2017
- García-Mata, I.; Roncaglia, A. J.; Wisniacki, D. A.
- EPL (Europhysics Letters), Vol. 120, Issue 3
Measuring the Characteristic Function of the Work Distribution
journal, June 2013
- Mazzola, L.; De Chiara, G.; Paternostro, M.
- Physical Review Letters, Vol. 110, Issue 23
Principle of minimal work fluctuations
journal, August 2015
- Xiao, Gaoyang; Gong, Jiangbin
- Physical Review E, Vol. 92, Issue 2
Extracting Quantum Work Statistics and Fluctuation Theorems by Single-Qubit Interferometry
journal, June 2013
- Dorner, R.; Clark, S. R.; Heaney, L.
- Physical Review Letters, Vol. 110, Issue 23
Entropy production fluctuation theorem and the nonequilibrium work relation for free energy differences
journal, September 1999
- Crooks, Gavin E.
- Physical Review E, Vol. 60, Issue 3
Time-dependent manifestations of quantum chaos
journal, September 1991
- Wilkie, Joshua; Brumer, Paul
- Physical Review Letters, Vol. 67, Issue 10, p. 1185-1188
Functional methods in thermofield dynamics: A real-time perturbation theory for quantum statistical mechanics
journal, June 1983
- Semenoff, G. W.; Umezawa, H.
- Nuclear Physics B, Vol. 220, Issue 2
Thermodynamics of quantum information scrambling
journal, June 2017
- Campisi, Michele; Goold, John
- Physical Review E, Vol. 95, Issue 6
Quantum supremacy of many-particle thermal machines
journal, July 2016
- Jaramillo, J.; Beau, M.; Campo, A. del
- New Journal of Physics, Vol. 18, Issue 7
Fluctuation theorems: Work is not an observable
journal, May 2007
- Talkner, Peter; Lutz, Eric; Hänggi, Peter
- Physical Review E, Vol. 75, Issue 5
Dynamics of Loschmidt echoes and fidelity decay
journal, November 2006
- Gorin, Thomas; Prosen, Tomaž; Seligman, Thomas H.
- Physics Reports, Vol. 435, Issue 2-5
Very long time scales and black hole thermal equilibrium
journal, November 2003
- Barbón, José L. F.; Rabinovici, Eliezer
- Journal of High Energy Physics, Vol. 2003, Issue 11
Criticality revealed through quench dynamics in the Lipkin-Meshkov-Glick model
journal, November 2016
- Campbell, Steve
- Physical Review B, Vol. 94, Issue 18
Non-equilibrium thermodynamics of harmonically trapped bosons
journal, October 2016
- García-March, Miguel Ángel; Fogarty, Thomás; Campbell, Steve
- New Journal of Physics, Vol. 18, Issue 10
Quantum-to-classical transition in the work distribution for chaotic systems
journal, May 2017
- García-Mata, Ignacio; Roncaglia, Augusto J.; Wisniacki, Diego A.
- Physical Review E, Vol. 95, Issue 5
Statistics of the Work Done on a Quantum Critical System by Quenching a Control Parameter
journal, September 2008
- Silva, Alessandro
- Physical Review Letters, Vol. 101, Issue 12
Scrambling the spectral form factor: Unitarity constraints and exact results
journal, June 2017
- del Campo, A.; Molina-Vilaplana, J.; Sonner, J.
- Physical Review D, Vol. 95, Issue 12
Thermodynamic cost for classical counterdiabatic driving
journal, November 2017
- Bravetti, Alessandro; Tapias, Diego
- Physical Review E, Vol. 96, Issue 5
Quantum thermodynamics
journal, February 2001
- Hoffmann, K. H.
- Annalen der Physik, Vol. 10, Issue 1-2
Digital Quantum Simulation of Spin Models with Circuit Quantum Electrodynamics
text, January 2015
- Yves, Salathé,; Mintu, Mondal,; Markus, Oppliger,
- ETH Zurich
Environment-Independent Decoherence Rate in Classically Chaotic Systems
text, January 2001
- Jalabert, Rodolfo A.; Pastawski, Horacio M.
- The American Physical Society
Black holes as mirrors: quantum information in random subsystems
text, January 2007
- Hayden, Patrick; Preskill, John
- arXiv
The Statistics of the Work Done on a Quantum Critical System by Quenching a Control Parameter
text, January 2008
- Silva, Alessandro
- arXiv
Generalized Clausius inequality for nonequilibrium quantum processes
text, January 2010
- Deffner, Sebastian; Lutz, Eric
- arXiv
Extracting quantum work statistics and fluctuation theorems by single qubit interferometry
text, January 2013
- Dorner, R.; Clark, S. R.; Heaney, L.
- arXiv
Irreversible work and inner friction in quantum thermodynamic processes
text, January 2014
- Plastina, F.; Alecce, A.; Apollaro, T. J. G.
- arXiv
Work measurement as a generalized quantum measurement
text, January 2014
- Roncaglia, Augusto J.; Cerisola, Federico; Paz, Juan Pablo
- arXiv
Local Operators in the Eternal Black Hole
text, January 2015
- Papadodimas, Kyriakos; Raju, Suvrat
- arXiv
Digital quantum simulation of spin models with circuit quantum electrodynamics
text, January 2015
- Salathé, Y.; Mondal, M.; Oppliger, M.
- arXiv
The role of quantum information in thermodynamics --- a topical review
text, January 2015
- Goold, John; Huber, Marcus; Riera, Arnau
- arXiv
Quantum Supremacy of Many-Particle Thermal Machines
text, January 2015
- Jaramillo, Juan; Beau, Mathieu; del Campo, Adolfo
- arXiv
Measuring out-of-time-order correlations and multiple quantum spectra in a trapped ion quantum magnet
text, January 2016
- Gärttner, Martin; Bohnet, Justin G.; Safavi-Naini, Arghavan
- arXiv
Jarzynski-like equality for the out-of-time-ordered correlator
text, January 2016
- Halpern, Nicole Yunger
- arXiv
Measuring out-of-time-order correlators on a nuclear magnetic resonance quantum simulator
text, January 2016
- Li, Jun; Fan, Ruihua; Wang, Hengyan
- arXiv
Thermodynamics of quantum information scrambling
text, January 2016
- Campisi, Michele; Goold, John
- arXiv
Black Holes and Random Matrices
text, January 2016
- Cotler, Jordan S.; Gur-Ari, Guy; Hanada, Masanori
- arXiv
Quantum work statistics, Loschmidt echo and information scrambling
text, January 2017
- Chenu, Aurélia; Egusquiza, Iñigo L.; Molina-Vilaplana, Javier
- arXiv
Environment-independent decoherence rate in classically chaotic systems
text, January 2000
- Jalabert, Rodolfo A.; Pastawski, Horacio M.
- arXiv
Fluctuation theorems: Work is not an observable
text, January 2007
- Talkner, Peter; Lutz, Eric; Hanggi, Peter
- arXiv
Very Long Time Scales and Black Hole Thermal Equilibrium
text, January 2003
- Barbon, J. L. F.; Rabinovici, E.
- arXiv
Integration with respect to the Haar measure on unitary, orthogonal and symplectic group
text, January 2004
- Collins, Benoit; Sniady, Piotr
- arXiv
On long time unitarity restoring processes in the presence of eternal black holes
journal, June 2004
- Barbón, J. L. F.; Rabinovici, E.
- Fortschritte der Physik, Vol. 52, Issue 67
Work measurement as a generalized quantum measurement
text, January 2014
- Roncaglia, Augusto J.; Cerisola, Federico; Paz, Juan Pablo
- arXiv
Works referencing / citing this record:
Work statistics for sudden quenches in interacting quantum many-body systems
journal, November 2019
- Arrais, Eric G.; Wisniacki, Diego A.; Roncaglia, Augusto J.
- Physical Review E, Vol. 100, Issue 5
Work statistics for sudden quenches in interacting quantum many-body systems
journal, November 2019
- Arrais, Eric G.; Wisniacki, Diego A.; Roncaglia, Augusto J.
- Physical Review E, Vol. 100, Issue 5
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