Relaxation dynamics of local observables in integrable systems

• Published in: Journal of physics. A, Mathematical and theoretical Vol. 48; no. 43; pp. 43 - 9
• Main Authors: Nardis, J De, Piroli, L, Caux, J-S
• Format: Journal Article
• Language: English
• Published: IOP Publishing 30.10.2015
• Subjects: Bose-Einstein condensates; Dynamical systems; Dynamics; Evolution; integrable models; Mathematical analysis; Mathematical models; out-of-equilibrium; Power law; relaxation processes; Steady state; thermodynamics
• ISSN: 1751-8113; 1751-8121
• DOI: 10.1088/1751-8113/48/43/43FT01

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 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 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.