Exact nonequilibrium dynamics of finite-temperature Tonks-Girardeau gases

TL;DR

This paper presents an exact method for analyzing the finite-temperature nonequilibrium dynamics of strongly interacting one-dimensional bosonic gases in the Tonks-Girardeau regime, using a Fredholm determinant approach and Bose-Fermi mapping.

Contribution

The authors develop an exact, computationally efficient approach to solve finite-temperature nonequilibrium dynamics of Tonks-Girardeau gases, extending previous methods to include temperature effects.

Findings

Successfully modeled collective breathing mode oscillations.

Analyzed collisional dynamics in Newton's cradle setup.

Demonstrated computational efficiency and accuracy of the method.

Abstract

Describing finite-temperature nonequilibrium dynamics of interacting many-particle systems is a notoriously challenging problem in quantum many-body physics. Here we provide an exact solution to this problem for a system of strongly interacting bosons in one dimension in the Tonks-Girardeau regime of infinitely strong repulsive interactions. Using the Fredholm determinant approach and the Bose-Fermi mapping we show how the problem can be reduced to a single-particle basis, wherein the finite-temperature effects enter the solution via an effective "dressing" of the single-particle wavefunctions by the Fermi-Dirac occupation factors. We demonstrate the utility of our approach and its computational efficiency in two nontrivial out-of-equilibrium scenarios: collective breathing mode oscillations in a harmonic trap and collisional dynamics in the Newton's cradle setting involving real-time evolution in a periodic Bragg potential.