Exact methods in analysis of nonequilibrium dynamics of integrable models: application to the study of correlation functions in nonequilibrium 1D Bose gas

TL;DR

This paper develops a numerical method based on form factors and intertwining operators to analyze the nonequilibrium dynamics of a 1D Bose gas with strong interactions, revealing transient crystal-like correlations.

Contribution

It introduces a novel numerical approach combining form-factor and intertwining operator methods for studying nonequilibrium dynamics in integrable models.

Findings

Observation of transient crystal-like correlations during evolution

Development of a numerical procedure for summing over intermediate states

Analysis focused on strong repulsive interactions and specific initial states

Abstract

In this paper we study nonequilibrium dynamics of one dimensional Bose gas from the general perspective of dynamics of integrable systems. After outlining and critically reviewing methods based on inverse scattering transform, intertwining operators, q-deformed objects, and extended dynamical conformal symmetry, we focus on the form-factor based approach. Motivated by possible applications in nonlinear quantum optics and experiments with ultracold atoms, we concentrate on the regime of strong repulsive interactions. We consider dynamical evolution starting from two initial states: a condensate of particles in a state with zero momentum and a condensate of particles in a gaussian wavepacket in real space. Combining the form-factor approach with the method of intertwining operator we develop a numerical procedure which allows explicit summation over intermediate states and analysis of the time evolution of non-local density-density correlation functions. In both cases we observe a tendency toward formation of crystal-like correlations at intermediate time scales.