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Density matrix of chaotic quantum systems

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Abstract

The nonequilibrium dynamics in chaotic quantum systems denies a fully understanding up to now, even if thermalization in the long-time asymptotic state has been explained by the eigenstate thermalization hypothesis which assumes a universal form of the observable matrix elements in the eigenbasis of Hamiltonian. It was recently proposed that the density matrix elements have also a universal form, which can be used to understand the nonequilibrium dynamics at the whole time scale, from the transient regime to the long-time steady limit. In this paper, we numerically test these assumptions for density matrix in the models of spins.

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References

  1. I. Bloch, J. Dalibard, W. Zwerger, Rev. Mod. Phys. 80, 885 (2008)

    Article  ADS  Google Scholar 

  2. A. Polkovnikov, K. Sengupta, A. Silva, M. Vengalattore, Rev. Mod. Phys. 83, 863 (2011)

    Article  ADS  Google Scholar 

  3. J. Eisert, M. Friesdorf, C. Gogolin, Nat. Phys. 11, 124 (2015)

    Article  Google Scholar 

  4. M. Rigol, V. Dunjko, V. Yurovsky, M. Olshanii, Phys. Rev. Lett. 98, 050405 (2007)

    Article  ADS  Google Scholar 

  5. M. Rigol, V. Dunjko, M. Olshanii, Nature 452, 854 (2008)

    Article  ADS  Google Scholar 

  6. J. von Neumann, Z. Phys. 57, 30 (1929)

    Article  Google Scholar 

  7. S. Goldstein, J.L. Lebowitz, R. Tumulka, N. Zanghì, Eur. Phys. J. H 35, 173 (2010)

    Article  Google Scholar 

  8. E. Wigner, Ann. Math. 62, 548 (1955)

    Article  MathSciNet  Google Scholar 

  9. E. Wigner, Ann. Math. 65, 203 (1957)

    Article  MathSciNet  Google Scholar 

  10. E. Wigner, Ann. Math. 67, 325 (1958)

    Article  MathSciNet  Google Scholar 

  11. N. Rosenzweig, C.E. Porter, Phys. Rev. 120, 1698 (1960)

    Article  ADS  Google Scholar 

  12. T.A. Brody, J. Flores, J.B. French, P. Mello, A. Pandey, S.S. Wong, Rev. Mod. Phys. 53, 385 (1981)

    Article  ADS  Google Scholar 

  13. O. Bohigas, M.-J. Giannoni, C. Schmit, Phys. Rev. Lett. 52, 1 (1984)

    Article  ADS  MathSciNet  Google Scholar 

  14. M.R. Schroeder, J. Audio. Eng. Soc. 35, 299 (1987)

    MathSciNet  Google Scholar 

  15. T. Guhr, A. Müller-Groeling, H.A. Weidenmüller, Phys. Rep. 299, 189 (1998)

    Article  ADS  MathSciNet  Google Scholar 

  16. M.V. Berry, M. Tabor, Proc. R. Soc. A 356, 375 (1977)

    ADS  Google Scholar 

  17. J.M. Deutsch, Phys. Rev. A 43, 2046 (1991)

    Article  ADS  Google Scholar 

  18. M. Srednicki, Phys. Rev. E 50, 888 (1994)

    Article  ADS  Google Scholar 

  19. M. Srednicki, J. Phys. A: Math. Gen. 32, 1163 (1999)

    Article  ADS  MathSciNet  Google Scholar 

  20. L. D’Alessio, Y. Kafri, A. Polkovnikov, M. Rigol, Adv. Phys. 65, 239 (2016)

    Article  ADS  Google Scholar 

  21. K.R. Fratus, M. Srednicki, Phys. Rev. E 92, 040103 (2015)

    Article  ADS  Google Scholar 

  22. I.V. Gornyi, A.D. Mirlin, D.G. Polyakov, Phys. Rev. Lett. 95, 206603 (2005)

    Article  ADS  Google Scholar 

  23. D. Basko, I. Aleiner, B. Altshuler, Ann. Phys. 321, 1126 (2006)

    Article  ADS  Google Scholar 

  24. P. Wang, J. Stat. Mech. 2017, 093105 (2017)

    Article  Google Scholar 

  25. L.F. Santos, A. Polkovnikov, M. Rigol, Phys. Rev. Lett. 107, 040601 (2011)

    Article  ADS  Google Scholar 

  26. V.V. Flambaum, F.M. Izrailev, Phys. Rev. E 56, 5144 (1997)

    Article  ADS  Google Scholar 

  27. V. Kravtsov, arXiv:0911.0639 (2012)

  28. M. Hartmann, G. mahler, O. Hess, Lett. Math. Phys. 68, 103 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  29. L. Foini, J. Kurchan, Phys. Rev. E 99, 042139 (2019)

    Article  ADS  Google Scholar 

  30. R. Mondaini, M. Rigol, Phys. Rev. E 96, 012157 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  31. R. Mondaini, K.R. Fratus, M. Srednicki, M. Rigol, Phys. Rev. E 93, 032104 (2016)

    Article  ADS  Google Scholar 

  32. C.L. Bertrand, A.M. García-García, Phys. Rev. B 94, 144201 (2016)

    Article  ADS  Google Scholar 

Download references

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Correspondence to Pei Wang.

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Yang, X., Wang, P. Density matrix of chaotic quantum systems. Eur. Phys. J. B 93, 198 (2020). https://doi.org/10.1140/epjb/e2020-10074-9

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  • DOI: https://doi.org/10.1140/epjb/e2020-10074-9

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