Relaxation dynamics of a mobile impurity injected into a one-dimensional Bose gas

TL;DR

This paper investigates the nonequilibrium relaxation dynamics of a mobile impurity in a one-dimensional Bose gas, revealing regimes of constant velocity, shock wave emission, and complex oscillatory behaviors depending on impurity mass and interactions.

Contribution

It introduces a detailed analysis of impurity relaxation regimes in 1D Bose gases using the Gross-Pitaevskii framework, highlighting new phenomena like shock waves and metastable states.

Findings

Impurity velocity remains constant over a range of initial velocities.

Heavy impurities exhibit damped velocity oscillations and complex relaxation behaviors.

Cusps and metastable branches in energy-momentum relations lead to soliton emission and altered motion.

Abstract

The nonequilibrium dynamics of an impurity immersed with a finite velocity into a one-dimensional system of weakly interacting bosons is studied within the framework of the time-dependent Gross-Pitaevskii equation. We uncover and characterize different regimes of relaxation dynamics. We find that the final impurity velocity remains constant in a large interval of sufficiently big and realistic initial velocities. The underlying physical mechanism is the emission of the dispersive density shock waves that carry away the excess of the initial impurity momentum, while locally the system remains in the same stationary state. In contrast, a heavy impurity with the same coupling constant relaxes differently and the regime of constant final velocity disappears. Furthermore, a fast heavy impurity exhibits damped velocity oscillations in time before reaching a stationary state. This process is accompanied by the oscillations of the local depletion of the boson density around the impurity, until their positions coincide and they continue the motion together. Decreasing the impurity-boson coupling or increasing the strength of repulsion between bosons, the oscillations get amplified. In the case of a heavy impurity with the mass bigger than the critical one, the ground state energy as a function of momentum exhibits cusps and metastable branches. We show that they manifest themselves by a soliton emission, a considerable slowing down of the relaxation, and a change of the impurity direction of motion with respect to the initial one.