×
de Oliveira, Thiago R.; Charalambous, Christos; Jonathan, Daniel; Lewenstein, Maciej; Riera, Arnau

Equilibration time scales in closed many-body quantum systems. (English) Zbl 07853216

New J. Phys. 20, No. 3, Article ID 033032, 25 p. (2018).
Summary: We show that the physical mechanism for the equilibration of closed quantum systems is dephasing, and identify the energy scales that determine the equilibration timescale of a given observable. For realistic physical systems (e.g those with local Hamiltonians), our arguments imply timescales that do not increase with the system size, in contrast to previously known upper bounds. In particular we show that, for such Hamiltonians, the matrix representation of local observables in the energy basis is banded, and that this property is crucial in order to derive equilibration times that are non-negligible in macroscopic systems. Finally, we give an intuitive interpretation to recent theorems on equilibration time-scales.

Cited in 4 Documents

MSC:

81V70 Many-body theory; quantum Hall effect
Cite Review PDF
Full Text: DOI arXiv

References:

[1] Gogolin C and Eisert J 2016 Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems Rep. Prog. Phys.79 056001 · doi:10.1088/0034-4885/79/5/056001
[2] Reimann P 2007 Typicality for generalized microcanonical ensembles Phys. Rev. Lett.99 160404 · doi:10.1103/PhysRevLett.99.160404
[3] Goldstein S, Lebowitz J L, Tumulka R and Zanghì N 2006 Canonical typicality Phys. Rev. Lett.96 050403 · doi:10.1103/PhysRevLett.96.050403
[4] Popescu S, Short A J and Winter A 2006 Entanglement and the foundations of statistical mechanics Nat. Phys.2 754-8 · doi:10.1038/nphys444
[5] Reimann P 2008 Foundations of statistical mechanics under experimentally realistic conditions Phys. Rev. Lett.101 3 · doi:10.1103/PhysRevLett.101.190403
[6] Linden N, Popescu S, Short A J and Winter A 2009 Quantum mechanical evolution towards thermal equilibrium Phys. Rev. E 79 061103 · doi:10.1103/PhysRevE.79.061103
[7] Monnai T 2013 Generic evaluation of relaxation time for quantum many-body systems: analysis of the system size dependence J. Phys. Soc. Japan82 044006 · doi:10.7566/JPSJ.82.044006
[8] Brandão F G S L, Ćwikliński P, Horodecki M, Horodecki P, Korbicz J K and Mozrzymas M 2012 Convergence to equilibrium under a random hamiltonian Phys. Rev. E 86 031101 · doi:10.1103/PhysRevE.86.031101
[9] Cramer M 2012 Thermalization under randomized local hamiltonians New J. Phys.14 053051 · Zbl 1448.81100 · doi:10.1088/1367-2630/14/5/053051
[10] Masanes L, Roncaglia A J and Acín A 2013 Complexity of energy eigenstates as a mechanism for equilibration Phys. Rev. E 87 032137 · doi:10.1103/PhysRevE.87.032137
[11] Malabarba A S L, García-Pintos L P, Linden N, Farrelly T C and Short A J 2014 Quantum systems equilibrate rapidly for most observables Phys. Rev. E 90 012121 · doi:10.1103/PhysRevE.90.012121
[12] Goldstein S, Hara T and Tasaki H 2014 The approach to equilibrium in a macroscopic quantum system for a typical nonequilibrium subspace arXiv:1402.3380
[13] Goldstein S, Hara T and Tasaki H 2015 Extremely quick thermalization in a macroscopic quantum system for a typical nonequilibrium subspace New J. Phys.17 045002 · Zbl 1452.82011 · doi:10.1088/1367-2630/17/4/045002
[14] García-Pintos L P, Linden N, Malabarba A S L, Short A J and Winter A 2017 Equilibration time scales of physically relevant observables Phys. Rev. X 7 031027 · doi:10.1103/PhysRevX.7.031027
[15] Short A J and Farrelly T C 2012 Quantum equilibration in finite time New J. Phys.14 013063 · Zbl 1448.81406 · doi:10.1088/1367-2630/14/1/013063
[16] Farrelly T 2016 Equilibration of quantum gases New J. Phys.18 073014 · Zbl 1462.82025 · doi:10.1088/1367-2630/18/7/073014
[17] Reimann P 2016 Typical fast thermalization processes in closed many-body systems Nat. Commun.7 10821 · doi:10.1038/ncomms10821
[18] Balz B N and Reimann P 2017 Typical relaxation of isolated many-body systems which do not thermalize Phys. Rev. Lett.118 190601 · doi:10.1103/PhysRevLett.118.190601
[19] Santos L F and Torres-Herrera E J 2017 Nonequilibrium quantum dynamics of many-body systems arXiv:1706.02031
[20] Goldstein S, Hara T and Tasaki H 2013 On the time scales in the approach to equilibrium of macroscopic quantum systems Phys. Rev. Lett.111 140401 · doi:10.1103/PhysRevLett.111.140401
[21] Srednicki M 1994 Chaos and quantum thermalization Phys. Rev. E 50 901 · doi:10.1103/PhysRevE.50.888
[22] Wilming H, Goihl M, Krumnow C and Eisert J 2017 Towards local equilibration in closed interacting quantum many-body systems arXiv:1704.06291
[23] Arad I, Kuwahara T and Landau Z 2016 Connecting global and local energy distributions in quantum spin models on a lattice J. Stat. Mech. 2016 033301 · Zbl 1456.81320 · doi:10.1088/1742-5468/2016/03/033301
[24] Short A J 2011 Equilibration of quantum systems and subsystems New J. Phys.13 053009 · Zbl 1448.81405 · doi:10.1088/1367-2630/13/5/053009
[25] Reimann P 2010 Canonical thermalization New J. Phys.12 055027 · Zbl 1375.81157 · doi:10.1088/1367-2630/12/5/055027
[26] Fonda L, Ghirardi G C and Rimini A 1978 Decay theory of unstable quantum systems Rep. Prog. Phys.41 587 · doi:10.1088/0034-4885/41/4/003
[27] Robinett R W 2004 Quantum wave packet revivals Phys. Rep.392 1-119 · doi:10.1016/j.physrep.2003.11.002
[28] Eberly J H, Narozhny N B and Sanchez-Mondragon J J 1980 Periodic spontaneous collapse and revival in a simple quantum model Phys. Rev. Lett.44 1323 · Zbl 1404.81338 · doi:10.1103/PhysRevLett.44.1323
[29] Eberly J H, Narozhny N B and Sanchez-Mondragon J J 1981 Coherence versus incoherence: collapse and revival in a simple quantum model Phys. Rev. A 23 236 · doi:10.1103/PhysRevA.23.236
[30] Allen L and Eberly J H 1987 Optical Resonance and Two-Level Atoms (New York: Dover)
[31] Lifshitz E M and Pitaevskii L P 1958 Statistical Physics: Theory of the Condensed State(Course of Theoretical Physics vol 9) (Oxford: Pergamon) · Zbl 0080.19702
[32] Baym G and Pethick C 2004 Landau Fermi-Liquid Theory: Concepts and Applications (New York: Wiley-VCH)
[33] Polkovnikov A, Sengupta K, Silva A and Vengalattore M 2011 Colloquium: nonequilibrium dynamics of closed interacting quantum systems Rev. Mod. Phys.83 863 · doi:10.1103/RevModPhys.83.863
[34] Stein E M and Shakarchi R 2015 Fourier Analysis: an Introduction (Princeton, NJ: Princeton University Press)
[35] Eberlein W F 1949 Abstract ergodic theorems and weak almost periodic functions Trans. Amer. Math. Soc.67 217-40 · Zbl 0034.06404 · doi:10.1090/S0002-9947-1949-0036455-9
[36] Corduneanu C 2009 Almost Periodic Oscillation and Waves (Berlin: Springer) · Zbl 1163.34002 · doi:10.1007/978-0-387-09819-7
[37] Brandāo F G S L and Cramer M 2015 Equivalence of statistical mechanical ensembles for non-critical quantum systems arXiv:1502.03263
[38] D’Alessio L, Kafri Y, Polkovnikov A and Rigol M 2016 From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics Adv. Phys.65 239-362 · doi:10.1080/00018732.2016.1198134
[39] Haque M, Beugeling W and Moessner R 2015 Off-diagonal matrix elements of local operators in many-body quantum systems Phys. Rev. E 91 012144 · doi:10.1103/PhysRevE.91.012144
[40] Miranda Y M and Slade G 2011 The growth constants of lattice trees and lattice animals in high dimensions Electron. Commun. Probab.16 129 · Zbl 1225.60154 · doi:10.1214/ECP.v16-1612
[41] Perarnau-Llobet M, Wilming H, Riera A, Gallego R and Eisert J 2017 Fundamental corrections to work and power in the strong coupling regime arXiv:1704.05864
[42] Hastings M B and Koma T 2006 Spectral gap and exponential decay of correlations Commun. Math. Phys.265 781-804 · Zbl 1104.82010 · doi:10.1007/s00220-006-0030-4
[43] Kliesch M, Gogolin C, Kastoryano M J, Riera A and Eisert J 2014 Locality of temperature Phys. Rev. X 4 031019 · doi:10.1103/PhysRevX.4.031019
[44] Penrose M 1994 Self-avoiding walks and trees in spread-out lattices J. Stat. Phys.77 3 · Zbl 0838.60064 · doi:10.1007/BF02186829
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.