Single-particle density matrix for a time-dependent strongly interacting one-dimensional Bose gas

TL;DR

This paper develops a $1/c$-expansion method for the single-particle density matrix of a strongly interacting, time-dependent 1D Bose gas, providing an efficient numerical approach for studying its dynamics in the strong coupling regime.

Contribution

It introduces a novel $1/c$-expansion formalism and an efficient numerical algorithm for analyzing the dynamics of strongly interacting 1D Bose gases.

Findings

Derived a $1/c$-expansion for the density matrix.

Developed an efficient numerical algorithm.

Applied to contraction dynamics of localized wave packets.

Abstract

We derive a $1/c$-expansion for the single-particle density matrix of a strongly interacting time-dependent one-dimensional Bose gas, described by the Lieb-Liniger model ($c$ denotes the strength of the interaction). The formalism is derived by expanding Gaudin's Fermi-Bose mapping operator up to $1/c$-terms. We derive an efficient numerical algorithm for calculating the density matrix for time-dependent states in the strong coupling limit, which evolve from a family of initial conditions in the absence of an external potential. We have applied the formalism to study contraction dynamics of a localized wave packet upon which a parabolic phase is imprinted initially.