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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I. Bloch, J. Dalibard, W. Zwerger, Rev. Mod. Phys. 80, 885 (2008)
A. Polkovnikov, K. Sengupta, A. Silva, M. Vengalattore, Rev. Mod. Phys. 83, 863 (2011)
J. Eisert, M. Friesdorf, C. Gogolin, Nat. Phys. 11, 124 (2015)
M. Rigol, V. Dunjko, V. Yurovsky, M. Olshanii, Phys. Rev. Lett. 98, 050405 (2007)
M. Rigol, V. Dunjko, M. Olshanii, Nature 452, 854 (2008)
J. von Neumann, Z. Phys. 57, 30 (1929)
S. Goldstein, J.L. Lebowitz, R. Tumulka, N. Zanghì, Eur. Phys. J. H 35, 173 (2010)
E. Wigner, Ann. Math. 62, 548 (1955)
E. Wigner, Ann. Math. 65, 203 (1957)
E. Wigner, Ann. Math. 67, 325 (1958)
N. Rosenzweig, C.E. Porter, Phys. Rev. 120, 1698 (1960)
T.A. Brody, J. Flores, J.B. French, P. Mello, A. Pandey, S.S. Wong, Rev. Mod. Phys. 53, 385 (1981)
O. Bohigas, M.-J. Giannoni, C. Schmit, Phys. Rev. Lett. 52, 1 (1984)
M.R. Schroeder, J. Audio. Eng. Soc. 35, 299 (1987)
T. Guhr, A. Müller-Groeling, H.A. Weidenmüller, Phys. Rep. 299, 189 (1998)
M.V. Berry, M. Tabor, Proc. R. Soc. A 356, 375 (1977)
J.M. Deutsch, Phys. Rev. A 43, 2046 (1991)
M. Srednicki, Phys. Rev. E 50, 888 (1994)
M. Srednicki, J. Phys. A: Math. Gen. 32, 1163 (1999)
L. D’Alessio, Y. Kafri, A. Polkovnikov, M. Rigol, Adv. Phys. 65, 239 (2016)
K.R. Fratus, M. Srednicki, Phys. Rev. E 92, 040103 (2015)
I.V. Gornyi, A.D. Mirlin, D.G. Polyakov, Phys. Rev. Lett. 95, 206603 (2005)
D. Basko, I. Aleiner, B. Altshuler, Ann. Phys. 321, 1126 (2006)
P. Wang, J. Stat. Mech. 2017, 093105 (2017)
L.F. Santos, A. Polkovnikov, M. Rigol, Phys. Rev. Lett. 107, 040601 (2011)
V.V. Flambaum, F.M. Izrailev, Phys. Rev. E 56, 5144 (1997)
V. Kravtsov, arXiv:0911.0639 (2012)
M. Hartmann, G. mahler, O. Hess, Lett. Math. Phys. 68, 103 (2004)
L. Foini, J. Kurchan, Phys. Rev. E 99, 042139 (2019)
R. Mondaini, M. Rigol, Phys. Rev. E 96, 012157 (2017)
R. Mondaini, K.R. Fratus, M. Srednicki, M. Rigol, Phys. Rev. E 93, 032104 (2016)
C.L. Bertrand, A.M. García-García, Phys. Rev. B 94, 144201 (2016)
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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