Advertisement

The European Physical Journal Special Topics

, Volume 227, Issue 3–4, pp 323–333 | Cite as

Floquet–Gibbs state in open quantum systems

  • Tatsuhiko ShiraiEmail author
  • Takashi Mori
  • Seiji Miyashita
Regular Article
Part of the following topical collections:
  1. Quantum Systems In and Out of Equilibrium - Fundamentals, Dynamics and Applications

Abstract

We study long-time asymptotic states of periodically driven quantum systems coupled to a thermal bath. In order to describe a class of such a system, we introduce the Floquet–Gibbs state, i.e. the state whose density matrix is diagonalized in the basis of the Floquet state of the system Hamiltonian, and its diagonal element obeys the Boltzmann distribution over its Floquet quasienergy. We obtain sufficient conditions for the realization of the Floquet–Gibbs state in a system with infinitesimal system-bath coupling [T. Shirai et al., Phys. Rev. E 91, 030101 (2015)]. These conditions severely restrict a class of suitable physical models attaining the Floquet–Gibbs state. We also show that some of the conditions can be lifted by imposing conditions on timescales of the thermal bath with the aid of the truncated Floquet Hamiltonian in the Floquet–Magnus expansion [T. Shirai et al., New J. Phys. 18, 053008 (2016)]. In this paper, we give an overview of this theory and reconsider it by looking at the dynamics from a rotating frame.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    M. Bukov, L. D’Alessio, A. Polkovnikov, Adv. Phys. 64, 139 (2015) ADSCrossRefGoogle Scholar
  2. 2.
    A. Eckardt, E. Anisimovas, New J. Phys. 17, 093039 (2015) ADSCrossRefGoogle Scholar
  3. 3.
    M. Grifoni, P. Hänggi, Phys. Rep. 304, 229 (1998) ADSMathSciNetCrossRefGoogle Scholar
  4. 4.
    H.-P. Breuer, W. Huber, F. Petruccione, Phys. Rev. E 61, 4883 (2000) ADSCrossRefGoogle Scholar
  5. 5.
    W. Kohn, J. Stat. Phys. 103, 417 (2001) MathSciNetCrossRefGoogle Scholar
  6. 6.
    H.-P. Breuer, F. Petruccione, The theory of open quantum systems (Oxford University Press, Oxford, 2002) Google Scholar
  7. 7.
    R. Ketzmerick, W. Wustmann, Phys. Rev. E 82, 021114 (2010) ADSMathSciNetCrossRefGoogle Scholar
  8. 8.
    M. Langemeyer, M. Holthaus, Phys. Rev. E 89, 012101 (2014) ADSCrossRefGoogle Scholar
  9. 9.
    T. Shirai, T. Mori, S. Miyashita, Phys. Rev. E 91, 030101 (2015) ADSMathSciNetCrossRefGoogle Scholar
  10. 10.
    R. Blümel, A. Buchleitner, R. Graham, L. Sirko, U. Smilansky, H. Walther, Phys. Rev. A 44, 4521 (1991) ADSCrossRefGoogle Scholar
  11. 11.
    T. Dittrich, B. Oelschlägel, P. Hänggi, EPL 22, 5 (1993) ADSCrossRefGoogle Scholar
  12. 12.
    B. Oelschlägel, T. Dittrich, P. Hänggi, Acta Phys Pol. B 24, 845 (1993) Google Scholar
  13. 13.
    S. Gasparinetti, P. Solinas, S. Pugnetti, R. Fazio, J. Pekola, Phys. Rev. Lett. 110, 150403 (2013) ADSCrossRefGoogle Scholar
  14. 14.
    T. Shirai, J. Thingna, T. Mori, S. Denisov, P. Hänggi, S. Miyashita, New J. Phys. 18, 053008 (2016) ADSCrossRefGoogle Scholar
  15. 15.
    R. Kubo, J. Phys. Soc. Jpn. 12, 570 (1957) ADSCrossRefGoogle Scholar
  16. 16.
    T. Mori, T. Kuwahara, K. Saito, Phys. Rev. Lett. 116, 120401 (2016) ADSCrossRefGoogle Scholar
  17. 17.
    A. Lazarides, A. Das, R. Moessner, Phys. Rev. E 90, 012110 (2014) ADSCrossRefGoogle Scholar
  18. 18.
    L. D’Alessio, M. Rigol, Phys. Rev. X 4, 041048 (2014) Google Scholar
  19. 19.
    P. Ponte, A. Chandran, Z. Papić, D.A. Abanin, Ann. Phys. 353, 196 (2015) ADSCrossRefGoogle Scholar
  20. 20.
    S. Blanes, F. Casas, J.A. Oteo, J. Ros, Phys. Rep. 470, 151 (2009) ADSMathSciNetCrossRefGoogle Scholar
  21. 21.
    T. Kuwahara, T. Mori, K. Saito, Ann. Phys. 367, 96 (2016) ADSCrossRefGoogle Scholar
  22. 22.
    D. Abanin, W. De Roeck, W.W. Ho, F. Huveneers, Commun. Math. Phys. 354, 809 (2017) ADSCrossRefGoogle Scholar
  23. 23.
    T. Mori, S. Miyashita, J. Phys. Soc. Jpn. 77, 124005 (2008) ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Tatsuhiko Shirai
    • 1
    Email author
  • Takashi Mori
    • 2
  • Seiji Miyashita
    • 2
  1. 1.The Institute for Solid State Physics, The University of TokyoTokyoJapan
  2. 2.Department of PhysicsGraduate School of Science, The University of TokyoTokyoJapan

Personalised recommendations