Time-dependent evolution of two coupled Luttinger liquids

TL;DR

This paper analytically studies the time evolution of two coupled Luttinger liquids after an interaction quench, revealing that long-time correlations differ from equilibrium predictions and discussing experimental implications.

Contribution

It provides an exact analytical solution for the dynamics of coupled Luttinger liquids post-quench using bosonization, highlighting non-equilibrium critical exponents.

Findings

Long-time correlation exponents differ from equilibrium values.

Exact analytical expressions for time-dependent correlation functions.

Implications for experimental measurements of non-equilibrium Luttinger liquids.

Abstract

We consider two disconnected Luttinger liquids which are coupled at $t=0$ through chiral density-density interactions. Both for $t<0$ and $t \geq 0$ the system is exactly solvable by means of bosonization and this allows to evaluate analytically the time-dependence of correlation functions. We find that in the long-time limit the critical exponent governing the one-particle correlation function differs from the exponent dictated by the equilibrium ground state of the coupled system. We also discuss how this reflects on some physical quantities which are accessible in real experiments.