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We study the non-equilibrium dynamics of the Luttinger model after a quantumquench, when the initial state is a finite temperature thermal equilibriumstate. The diagonal elements of the density matrix in the steady state showthermal features for high temperature initial states only, otherwise retainhighly non-thermal character. The time evolution of Uhlmann fidelity, whichmeasures the distance between the time evolved and initial states, is evaluatedfor arbitrary initial temperatures and quench protocols. In the long timelimit, the overlap between the time evolved and initial system decreasesexponentially with the temperature with a universal prefactor. Withinperturbation theory, the statistics of final total energy and work arenumerically evaluated in the case of a sudden quench, which yield identicaldistributions at zero temperature. In both statistics, temperature effects aremore significant in small systems. The Dirac-delta peak at the adiabatic groundstate energy remains present in the probability distribution of the totalenergy, but disappears from the work distribution at non-zero initialtemperatures.

Quantum quench in the Luttinger model with finite temperature initial state