Long time thermal asymptotics of nonlinear Luttinger liquid from inverse scattering

Abstract

I derive a Fredholm determinant for the thermal correlator of vertex operators with a conformally invariant density matrix and nonlinear time evolution. Using the method of nonlinear steepest descent I find the long time asymptotics at finite temperature. The asymptotics display exponentially small corrections in temperature to the finite temperature mobile impurity phenomenology.

18 pages, 1 figure. Submission to SciPost

References in corpus (4)

• Dynamical Correlations after a Quantum Quench
• Dynamic response of one-dimensional interacting fermions
• Dynamical structure factor of one-dimensional Bose gases: experimental signatures of beyond-Luttinger liquid physics
• Exact exponents of edge singularities in dynamic correlation functions of 1D Bose gas