1307.7582 (Ádám Bácsi et al.)

Quantum quench in Luttinger liquids with finite temperature initial
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Ádám Bácsi, Balázs Dóra

We study the non-equilibrium dynamics of Luttinger liquids after a quantum quench, when the initial state is a finite temperature thermal equilibrium state. We start by determining the diagonal elements of the density matrix in the steady state, which do not show thermalization in general. The time evolution of fidelity, which measures the distance between the time evolved and initial states, is evaluated at finite temperatures using various generalizations of the zero temperature overlap. In the long time limit, the overlap between the time evolved and initial system decreases as the temperature rises. By determining the adiabatic fidelity, we show that the final state is less thermalized with higher initial temperature. Within perturbation theory, the statistics of final total energy and work are numerically evaluated in the case of a sudden quench. We show that at low temperature the final energy distribution function is the convolution of the initial energy distribution and the zero temperature work statistics. In both statistics, temperature effects are more significant in small systems.

View original: http://arxiv.org/abs/1307.7582