Exact relaxation dynamics of a localized many-body state in the 1D bose gas

TL;DR

This paper uses an exact numerical method to study the relaxation dynamics of a localized many-body state in a 1D Bose gas, revealing collapse, recurrence, and the influence of interactions on relaxation time.

Contribution

It provides an exact analysis of the time evolution of localized states in 1D Bose gases, connecting superpositions of excitations to soliton-like profiles and relaxation behaviors.

Findings

Localized state constructed by superposing one-hole excitations

Collapse into flat profile for large N (e.g., N=1000)

Recurrence phenomenon observed for small N (e.g., N=20)

Abstract

Through an exact method we numerically solve the time evolution of the density profile for an initially localized state in the one-dimensional bosons with repulsive short-range interactions. We show that a localized state with a density notch is constructed by superposing one-hole excitations. The initial density profile overlaps the plot of the squared amplitude of a dark soliton in the weak coupling regime. We observe the localized state collapsing into a flat profile in equilibrium for a large number of particles such as N=1000. The relaxation time increases as the coupling constant decreases, which suggests the existence of off-diagonal long-range order. We show a recurrence phenomenon for a small number of particles such as N=20.