Please wait a minute...
Frontiers of Physics

ISSN 2095-0462

ISSN 2095-0470(Online)

CN 11-5994/O4

邮发代号 80-965

2019 Impact Factor: 2.502

Frontiers of Physics  2018, Vol. 13 Issue (5): 130510   https://doi.org/10.1007/s11467-018-0822-y
  本期目录
Fluctuation relations for heat exchange in the generalized Gibbs ensemble
Bo-Bo Wei()
School of Physics and Energy, Shenzhen University, Shenzhen 518060, China
 全文: PDF(423 KB)  
Abstract

In this work, we investigate the heat exchange between two quantum systems whose initial equilibrium states are described by the generalized Gibbs ensemble. First, we generalize the fluctuation relations for heat exchange discovered by Jarzynski and Wójcik to quantum systems prepared in the equilibrium states described by the generalized Gibbs ensemble at various generalized temperatures. Secondly, we extend the connections between heat exchange and the Rényi divergences to quantum systems under generic initial conditions. These relations are applicable for quantum systems with conserved quantities and universally valid for quantum systems in the integrable and chaotic regimes.

Key wordsexchange fluctuation relation    generalized Gibbs ensemble
收稿日期: 2018-04-18      出版日期: 2018-09-10
Corresponding Author(s): Bo-Bo Wei   
 引用本文:   
. [J]. Frontiers of Physics, 2018, 13(5): 130510.
Bo-Bo Wei. Fluctuation relations for heat exchange in the generalized Gibbs ensemble. Front. Phys. , 2018, 13(5): 130510.
 链接本文:  
https://academic.hep.com.cn/fop/CN/10.1007/s11467-018-0822-y
https://academic.hep.com.cn/fop/CN/Y2018/V13/I5/130510
1 C. Jarzynski and D. K. Wójcik, Classical and quantum fluctuation theorems for heat exchange, Phys. Rev. Lett. 92(23), 230602 (2004)
https://doi.org/10.1103/PhysRevLett.92.230602
2 B. B. Wei, Relations between heat exchange and the Rényi divergences, Phys. Rev. E 97(4), 042107 (2018)
https://doi.org/10.1103/PhysRevE.97.042107
3 A. Rényi, in: Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, University of California Press Press, 1961, pp 547–561
4 T. van Erven and P. Harremoes, Rényi divergence and Kullback–Leibler divergence, IEEE Trans. Inf. Theory 60(7), 3797 (2014)
https://doi.org/10.1109/TIT.2014.2320500
5 S. Beigi, Sandwiched Rényi divergence satisfies data processing inequality, J. Math. Phys. 54(12), 122202 (2013)
https://doi.org/10.1063/1.4838855
6 M. Müller-Lennert, F. Dupuis, O. Szehr, S. Fehr, and M. Tomamichel, On quantum Rényi entropies: A new generalization and some properties, J. Math. Phys. 54(12), 122203 (2013)
https://doi.org/10.1063/1.4838856
7 M. Esposito, U. Harbola, and S. Mukamel, Nonequilibrium fluctuations, fluctuation theorems, and counting statistics in quantum systems, Rev. Mod. Phys. 81(4), 1665 (2009)
https://doi.org/10.1103/RevModPhys.81.1665
8 C. Jarzynski, Equalities and inequalities: Irreversibility and the second law of thermodynamics at the nanoscale, Annu. Rev. Condens. Matter Phys. 2(1), 329 (2011)
https://doi.org/10.1146/annurev-conmatphys-062910-140506
9 M. Campisi, P. Hanggi, and P. Talkner, Quantum fluctuation relations: Foundations and applications, Rev. Mod. Phys. 83(3), 771 (2011)
https://doi.org/10.1103/RevModPhys.83.771
10 T. Kinoshita, T. Wenger, and D. S. Weiss, A quantum Newton’s cradle, Nature 440(7086), 900 (2006)
https://doi.org/10.1038/nature04693
11 M. Rigol, V. Dunjko, V. Yurovsky, and M. Olshanii, 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, Phys. Rev. Lett. 98(5), 050405 (2007)
https://doi.org/10.1103/PhysRevLett.98.050405
12 P. Calabrese, F. H. L. Essler, and M. Fagotti, Quantum quench in the transverse field Ising chain, Phys. Rev. Lett. 106(22), 227203 (2011)
https://doi.org/10.1103/PhysRevLett.106.227203
13 M. Gring, M. Kuhnert, T. Langen, T. Kitagawa, B. Rauer, M. Schreitl, I. Mazets, D. A. Smith, E. Demler, and J. Schmiedmayer, Relaxation and prethermalization in an isolated quantum system, Science 337(6100), 1318 (2012)
https://doi.org/10.1126/science.1224953
14 J. P. Ronzheimer, M. Schreiber, S. Braun, S. S. Hodgman, S. Langer, I. P. McCulloch, F. Heidrich-Meisner, I. Bloch, and U. Schneider, Expansion dynamics of interacting bosons in homogeneous lattices in one and two dimensions, Phys. Rev. Lett. 110(20), 205301 (2013)
https://doi.org/10.1103/PhysRevLett.110.205301
15 J. S. Caux and F. H. Essler, Time evolution of local observables after quenching to an integrable model, Phys. Rev. Lett. 110(25), 257203 (2013)
https://doi.org/10.1103/PhysRevLett.110.257203
16 L. Vidmar, J. P. Ronzheimer, M. Schreiber, S. Braun, S. S. Hodgman, S. Langer, F. Heidrich-Meisner, I. Bloch, and U. Schneider, Dynamical quasicondensation of hard-core bosons at finite momenta, Phys. Rev. Lett. 115(17), 175301 (2015)
https://doi.org/10.1103/PhysRevLett.115.175301
17 L. Vidmar, D. Iyer, and M. Rigol, Emergent eigenstate solution to quantum dynamics far from equilibrium, Phys. Rev. X 7(2), 021012 (2017)
https://doi.org/10.1103/PhysRevX.7.021012
18 C. Gogolin and J. Eisert, Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems, Rep. Prog. Phys. 79(5), 056001 (2016)
https://doi.org/10.1088/0034-4885/79/5/056001
19 L. Vidmar and M. Rigol, Generalized Gibbs ensemble in integrable lattice models, J. Stat. Mech. 2016(6), 064007 (2016)
https://doi.org/10.1088/1742-5468/2016/06/064007
20 T. Langen, S. Erne, R. Geiger, B. Rauer, T. Schweigler, M. Kuhnert, W. Rohringer, I. E. Mazets, T. Gasenzer, and J. Schmiedmayer, Experimental observation of a generalized Gibbs ensemble, Science 348(6231), 207 (2015)
https://doi.org/10.1126/science.1257026
21 L. E. Reichl, A Modern Course in Statistical Physics, Edward Arnold, Austin, TX, 1987
22 E. T. Jaynes, Information theory and statistical mechanics, Phys. Rev. 106(4), 620 (1957)
https://doi.org/10.1103/PhysRev.106.620
23 E. T. Jaynes, Information theory and statistical mechanics (II), Phys. Rev. 108(2), 171 (1957)
https://doi.org/10.1103/PhysRev.108.171
24 W. Yang, W. L. Ma, and R. B. Liu, Quantum manybody theory for electron spin decoherence in nanoscale nuclear spin baths, Rep. Prog. Phys. 80(1), 016001 (2017)
https://doi.org/10.1088/0034-4885/80/1/016001
25 B. B. Wei, and R. B. Liu, Lee-Yang zeros and critical times in decoherence of a probe spin coupled to a bath, Phys. Rev. Lett. 109(18), 185701 (2012)
https://doi.org/10.1103/PhysRevLett.109.185701
26 B. B. Wei, S. W. Chen, H. C. Po, and R. B. Liu, Phase transitions in the complex plane of a physical parameter, Sci. Rep. 4(1), 5202 (2015)
https://doi.org/10.1038/srep05202
27 B. B. Wei, Z. F. Jiang, and R. B. Liu, Thermodynamic holography, Sci. Rep. 5(1), 15077 (2015)
https://doi.org/10.1038/srep15077
28 X. H. Peng, H. Zhou, B. B. Wei, J. Y. Cui, J. F. Du, and R. B. Liu, Experimental observation of Lee–Yang zeros, Phys. Rev. Lett. 114(1), 010601 (2015)
https://doi.org/10.1103/PhysRevLett.114.010601
29 B. B. Wei, Probing Yang–Lee edge singularity by central spin decoherence, New J. Phys. 19(8), 083009 (2017)
https://doi.org/10.1088/1367-2630/aa77d6
30 B. B. Wei, Probing conformal invariant of non-unitary two dimensional system by central spin decoherence, Sci. Rep. 8(1), 3080 (2018)
https://doi.org/10.1038/s41598-018-21360-7
31 H. T. Quan, Z. Song, X. F. Liu, P. Zanardi, and C. P. Sun, Decay of Loschmidt echo enhanced by quantum criticality, Phys. Rev. Lett. 96(14), 140604 (2006)
https://doi.org/10.1103/PhysRevLett.96.140604
32 J. Zhang, X. Peng, N. Rajendran, and D. Suter, Detection of quantum critical points by a probe qubit, Phys. Rev. Lett. 100(10), 100501 (2008)
https://doi.org/10.1103/PhysRevLett.100.100501
33 S. W. Chen, Z. F. Jiang, and R. B. Liu, Quantum criticality at high temperature revealed by spin echo, New J. Phys. 15(4), 043032 (2013)
https://doi.org/10.1088/1367-2630/15/4/043032
34 B. B. Wei and M. B. Plenio, Relations between dissipated work in non-equilibrium process and the family of Rényi divergences, New J. Phys. 19(2), 023002 (2017)
https://doi.org/10.1088/1367-2630/aa579e
35 B. B. Wei, Links between dissipation and Rényi divergences in the PT-symmetric quantum mechanics, Phys. Rev. A 97(1), 012105 (2018)
https://doi.org/10.1103/PhysRevA.97.012105
36 B. B. Wei, Relations between dissipated work and Rényi divergences in the generalized Gibbs ensemble, Phys. Rev. A 97(4), 042132 (2018)
https://doi.org/10.1103/PhysRevA.97.042132
37 X. Y. Guo, et al., Demonstration of irreversibility and dissipation relation of thermodynamics with a superconducting qubit, arXiv: 1710.10234 (2017)
38 A. Wehrl, General properties of entropy, Rev. Mod. Phys. 50(2), 221 (1978)
https://doi.org/10.1103/RevModPhys.50.221
39 J. Goold, U. Poschinger, and K. Modi, Measuring heat exchange of a quantum process, Phys. Rev. E 90(2), 020101 (2014)
https://doi.org/10.1103/PhysRevE.90.020101
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed