Relaxation dynamics of local observables in integrable systems

E-ISSN： 1751-8121|48|43|43FT01-51

ISSN： 1751-8121

Source： Journal of Physics A: Mathematical and Theoretical, Vol.48, Iss.43, 2015-10, pp. : 43FT01-51

Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.

Previous Menu Next

Abstract

We show, using the quench action approach (Caux and Essler 2013 Phys. Rev. Lett. 110 257203), that the whole post-quench time evolution of an integrable system in the thermodynamic limit can be computed with a minimal set of data which are encoded in what we denote the generalized single-particle overlap coefficient &&dollar;{s}_{0}^{{{rm{Psi }}}_{0}}(lambda ).&dollar;; This function can be extracted from the thermodynamically leading part of the overlaps between the eigenstates of the model and the initial state. For a generic global quench the shape of &&dollar;{s}_{0}^{{{rm{Psi }}}_{0}}(lambda )&dollar;; in the low momentum limit directly gives the exponent for the power law decay to the effective steady state. As an example we compute the time evolution of the static density–density correlation in the interacting Lieb–Liniger gas after a quench from a Bose–Einstein condensate. This shows an approach to equilibrium with power law t −3 which turns out to be independent of the post-quench interaction and of the considered observable.