Measuring effective temperatures in a generalized Gibbs ensemble

Foini, Laura; Gambassi, Andrea; Konik, Robert; Cugliandolo, Leticia F.

doi:10.1103/PhysRevE.95.052116

Title: Measuring effective temperatures in a generalized Gibbs ensemble

Journal Article · Thu May 11 00:00:00 EDT 2017 · Physical Review E

DOI:https://doi.org/10.1103/PhysRevE.95.052116· OSTI ID:1412643

Foini, Laura ^[1]; Gambassi, Andrea ^[2]; Konik, Robert ^[3]; Cugliandolo, Leticia F. ^[4]

Univ. of Geneva (Switzerland). Dept. of Quantum Matter Physics; PSL Research Univ., Univ. of Paris-Diderot, Sorbonne Univ., UPMC Univ., Paris (France). Lab. of Statisical Physics and Dept. of Ecole Normale Superieure
International School for Advanced Studies and National Inst. of Nuclear Physics (INFN), Trieste (Italy)
Brookhaven National Lab. (BNL), Upton, NY (United States). CMPMS Division
Univ. Pierre et Marie Curie, Paris (France). Lab. of Theoretical Physics and High Energy

The local physical properties of an isolated quantum statistical system in the stationary state reached long after a quench are generically described by the Gibbs ensemble, which involves only its Hamiltonian and the temperature as a parameter. Additional quantities conserved by the dynamics intervene in the description of the stationary state, if the system is instead integrable. The resulting generalized Gibbs ensemble involves a number of temperature-like parameters, the determination of which is practically difficult. We argue that in a number of simple models these parameters can be effectively determined by using fluctuation-dissipation relationships between response and correlation functions of natural observables, quantities which are accessible in experiments.

View Accepted Manuscript (DOE)

View Accepted Manuscript (Publisher)

Cite

Export

Save

Research Organization:: Brookhaven National Lab. (BNL), Upton, NY (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES); National Science Foundation (NSF)

Grant/Contract Number:: SC0012704; AC02-98CH10886; PHY 11-25915

OSTI ID:: 1412643

Alternate ID(s):: OSTI ID: 1356738

Report Number(s):: BNL-114304-2017-JA; PLEEE8; R&D Project: PO015; KC0202030; TRN: US1800313

Journal Information:: Physical Review E, Vol. 95, Issue 5; ISSN 2470-0045

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

Citation Metrics:

Cited by: 19 works

Citation information provided by
Web of Science

References (35)

Hard-core bosons on optical superlattices: Dynamics and relaxation in the superfluid and insulating regimes Rigol, Marcos; Muramatsu, Alejandro; Olshanii, Maxim Physical Review A, Vol. 74, Issue 5 https://doi.org/10.1103/PhysRevA.74.053616	journal	November 2006
Quantum quenches in the transverse field Ising chain: II. Stationary state properties Calabrese, Pasquale; Essler, Fabian H. L.; Fagotti, Maurizio Journal of Statistical Mechanics: Theory and Experiment, Vol. 2012, Issue 07 https://doi.org/10.1088/1742-5468/2012/07/P07022	journal	July 2012
Thermalization and its mechanism for generic isolated quantum systems Rigol, Marcos; Dunjko, Vanja; Olshanii, Maxim Nature, Vol. 452, Issue 7189 https://doi.org/10.1038/nature06838	journal	April 2008
The Quench Action Caux, Jean-Sébastien Journal of Statistical Mechanics: Theory and Experiment, Vol. 2016, Issue 6 https://doi.org/10.1088/1742-5468/2016/06/064006	journal	June 2016
Introduction to ‘Quantum Integrability in Out of Equilibrium Systems’ Calabrese, Pasquale; Essler, Fabian H. L.; Mussardo, Giuseppe Journal of Statistical Mechanics: Theory and Experiment, Vol. 2016, Issue 6 https://doi.org/10.1088/1742-5468/2016/06/064001	journal	June 2016
Mode-Coupling-Induced Dissipative and Thermal Effects at Long Times after a Quantum Quench Mitra, Aditi; Giamarchi, Thierry Physical Review Letters, Vol. 107, Issue 15 https://doi.org/10.1103/PhysRevLett.107.150602	journal	October 2011
Analytic results for a quantum quench from free to hard-core one-dimensional bosons Kormos, Márton; Collura, Mario; Calabrese, Pasquale Physical Review A, Vol. 89, Issue 1 https://doi.org/10.1103/PhysRevA.89.013609	journal	January 2014
Ageing properties of critical systems Calabrese, Pasquale; Gambassi, Andrea Journal of Physics A: Mathematical and General, Vol. 38, Issue 18 https://doi.org/10.1088/0305-4470/38/18/R01	journal	April 2005
Colloquium : Nonequilibrium dynamics of closed interacting quantum systems Polkovnikov, Anatoli; Sengupta, Krishnendu; Silva, Alessandro Reviews of Modern Physics, Vol. 83, Issue 3 https://doi.org/10.1103/RevModPhys.83.863	journal	August 2011
Experimental observation of a generalized Gibbs ensemble Langen, T.; Erne, S.; Geiger, R. Science, Vol. 348, Issue 6231 https://doi.org/10.1126/science.1257026	journal	April 2015
Energy flow, partial equilibration, and effective temperatures in systems with slow dynamics Cugliandolo, Leticia F.; Kurchan, Jorge; Peliti, Luca Physical Review E, Vol. 55, Issue 4 https://doi.org/10.1103/PhysRevE.55.3898	journal	April 1997
Dynamics of a quantum phase transition and relaxation to a steady state Dziarmaga, Jacek Advances in Physics, Vol. 59, Issue 6 https://doi.org/10.1080/00018732.2010.514702	journal	September 2010
Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems Gogolin, Christian; Eisert, Jens Reports on Progress in Physics, Vol. 79, Issue 5 https://doi.org/10.1088/0034-4885/79/5/056001	journal	April 2016
Constructing the Generalized Gibbs Ensemble after a Quantum Quench Caux, Jean-Sébastien; Konik, Robert M. Physical Review Letters, Vol. 109, Issue 17 https://doi.org/10.1103/PhysRevLett.109.175301	journal	October 2012
Quantum quenches in extended systems Calabrese, Pasquale; Cardy, John Journal of Statistical Mechanics: Theory and Experiment, Vol. 2007, Issue 06 https://doi.org/10.1088/1742-5468/2007/06/P06008	journal	June 2007
Exact Analysis of an Interacting Bose Gas. I. The General Solution and the Ground State Lieb, Elliott H.; Liniger, Werner Physical Review, Vol. 130, Issue 4 https://doi.org/10.1103/PhysRev.130.1605	journal	May 1963
Solution for an interaction quench in the Lieb-Liniger Bose gas De Nardis, Jacopo; Wouters, Bram; Brockmann, Michael Physical Review A, Vol. 89, Issue 3 https://doi.org/10.1103/PhysRevA.89.033601	journal	March 2014
Thermalization in systems with bipartite eigenmode entanglement Chung, Ming-Chiang; Iucci, A.; Cazalilla, M. A. New Journal of Physics, Vol. 14, Issue 7 https://doi.org/10.1088/1367-2630/14/7/075013	journal	July 2012
Relaxation in a Completely Integrable Many-Body Quantum System: An Ab Initio Study of the Dynamics of the Highly Excited States of 1D Lattice Hard-Core Bosons Rigol, Marcos; Dunjko, Vanja; Yurovsky, Vladimir Physical Review Letters, Vol. 98, Issue 5 https://doi.org/10.1103/PhysRevLett.98.050405	journal	February 2007
Effective temperature from fluctuation-dissipation theorem in systems with bipartite eigenmode entanglement Bortolin, T. S.; Iucci, A. Physical Review B, Vol. 91, Issue 2 https://doi.org/10.1103/PhysRevB.91.024301	journal	January 2015
Equilibration and coarsening in the quantum $O (N)$ model at infinite $N$ Chandran, Anushya; Nanduri, Arun; Gubser, S. S. Physical Review B, Vol. 88, Issue 2 https://doi.org/10.1103/PhysRevB.88.024306	journal	July 2013
Fluctuation-Dissipation Theorem in an Isolated System of Quantum Dipolar Bosons after a Quench Khatami, Ehsan; Pupillo, Guido; Srednicki, Mark Physical Review Letters, Vol. 111, Issue 5 https://doi.org/10.1103/PhysRevLett.111.050403	journal	July 2013
Fluctuation-dissipation relations and critical quenches in the transverse field Ising chain Foini, Laura; Cugliandolo, Leticia F.; Gambassi, Andrea Physical Review B, Vol. 84, Issue 21 https://doi.org/10.1103/PhysRevB.84.212404	journal	December 2011
Separation of Time Scales in a Quantum Newton’s Cradle van den Berg, R.; Wouters, B.; Eliëns, S. Physical Review Letters, Vol. 116, Issue 22 https://doi.org/10.1103/PhysRevLett.116.225302	journal	June 2016
Dynamic correlations, fluctuation-dissipation relations, and effective temperatures after a quantum quench of the transverse field Ising chain Foini, Laura; Cugliandolo, Leticia F.; Gambassi, Andrea Journal of Statistical Mechanics: Theory and Experiment, Vol. 2012, Issue 09 https://doi.org/10.1088/1742-5468/2012/09/P09011	journal	September 2012
On the definition of a unique effective temperature for non-equilibrium critical systems Calabrese, Pasquale; Gambassi, Andrea Journal of Statistical Mechanics: Theory and Experiment, Vol. 2004, Issue 07 https://doi.org/10.1088/1742-5468/2004/07/P07013	journal	July 2004
Complete Generalized Gibbs Ensembles in an Interacting Theory Ilievski, E.; De Nardis, J.; Wouters, B. Physical Review Letters, Vol. 115, Issue 15 https://doi.org/10.1103/PhysRevLett.115.157201	journal	October 2015
Aging and coarsening in isolated quantum systems after a quench: Exact results for the quantum $O (N)$ model with $N$ $\to$ $\infty$ Maraga, Anna; Chiocchetta, Alessio; Mitra, Aditi Physical Review E, Vol. 92, Issue 4 https://doi.org/10.1103/PhysRevE.92.042151	journal	October 2015
Quasilocal charges in integrable lattice systems Ilievski, Enej; Medenjak, Marko; Prosen, Tomaž Journal of Statistical Mechanics: Theory and Experiment, Vol. 2016, Issue 6 https://doi.org/10.1088/1742-5468/2016/06/064008	journal	June 2016
Exact Analysis of an Interacting Bose Gas. II. The Excitation Spectrum Lieb, Elliott H. Physical Review, Vol. 130, Issue 4 https://doi.org/10.1103/PhysRev.130.1616	journal	May 1963
Quantum statistical mechanics in a closed system Deutsch, J. M. Physical Review A, Vol. 43, Issue 4 https://doi.org/10.1103/PhysRevA.43.2046	journal	February 1991
Chaos and quantum thermalization Srednicki, Mark Physical Review E, Vol. 50, Issue 2 https://doi.org/10.1103/PhysRevE.50.888	journal	August 1994
Quantum quench from a thermal initial state Sotiriadis, S.; Calabrese, P.; Cardy, J. EPL (Europhysics Letters), Vol. 87, Issue 2 https://doi.org/10.1209/0295-5075/87/20002	journal	July 2009
The fluctuation-dissipation theorem Kubo, R. Reports on Progress in Physics, Vol. 29, Issue 1 https://doi.org/10.1088/0034-4885/29/1/306	journal	January 1966
The effective temperature Cugliandolo, Leticia F. Journal of Physics A: Mathematical and Theoretical, Vol. 44, Issue 48 https://doi.org/10.1088/1751-8113/44/48/483001	journal	November 2011

Cited By (4)

Momentum distribution and coherence of a weakly interacting Bose gas after a quench Martone, Giovanni I.; Larré, Pierre-Élie; Fabbri, Alessandro Physical Review A, Vol. 98, Issue 6 https://doi.org/10.1103/physreva.98.063617	journal	December 2018
Ballistic transport in the one-dimensional Hubbard model: The hydrodynamic approach Ilievski, Enej; De Nardis, Jacopo Physical Review B, Vol. 96, Issue 8 https://doi.org/10.1103/physrevb.96.081118	journal	August 2017
Ballistic transport in the one-dimensional Hubbard model: the hydrodynamic approach Ilievski, Enej; De Nardis, Jacopo arXiv https://doi.org/10.48550/arxiv.1706.05931	text	January 2017
Equilibration of Quasi-Integrable Systems Goldfriend, Tomer; Kurchan, Jorge arXiv https://doi.org/10.48550/arxiv.1810.06121	text	January 2018

Similar Records

Probing non-thermal density fluctuations in the one-dimensional Bose gas

Journal Article · Wed Sep 27 00:00:00 EDT 2017 · SciPost Physics · OSTI ID:1412643

De Nardis, Jacopo; Panfil, Milosz; Gambassi, Andrea; +3 more

Quasilocal charges and the generalized Gibbs ensemble in the Lieb-Liniger model

Journal Article · Wed Nov 21 00:00:00 EST 2018 · Physical Review E · OSTI ID:1412643

Palmai, Tamas; Konik, R. M.

Improving the sampling efficiency of the Grand Canonical Simulated Quenching approach

Technical Report · Wed Apr 04 00:00:00 EDT 2012 · OSTI ID:1412643

Perez, Danny; Vernon, Louis J

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY

Title: Measuring effective temperatures in a generalized Gibbs ensemble

Citation Formats

References (35)

Cited By (4)

Similar Records

Related Subjects