Exact results for nonequilibrium dynamics in Wigner phase space

TL;DR

This paper derives exact relationships for the time evolution of the Wigner function in one-dimensional quantum gases after sudden interaction changes, providing insights into nonequilibrium dynamics and scaling laws.

Contribution

It presents new exact formulas linking initial and time-evolved Wigner functions for various sudden quench scenarios in quantum gases.

Findings

Derived relationships between initial and evolved Wigner functions.

Established a scaling law for density matrix after trap frequency change.

Analyzed effects of interactions on the dynamical Wigner function.

Abstract

We study time evolution of Wigner function of an initially interacting one-dimensional quantum gas following the switch-off of the interactions. For the scenario where at $t=0$ the interactions are suddenly suppressed, we derive a relationship between the dynamical Wigner function and its initial value. A two-particle system initially interacting through two different interactions of Dirac delta type is examined. For a system of particles that is suddenly let to move ballistically (without interactions) in a harmonic trap in d dimensions, and using time evolution of one-body density matrix, we derive a relationship between the time dependent Wigner function and its initial value. Using the inverse Wigner transform we obtain, for an initially harmonically trapped noninteracting particles in $d$ dimensions, the scaling law satisfied by the density matrix at time $t$ after a sudden change of the trapping frequency. Finally, the effects of interactions are analyzed in the dynamical Wigner function.