Stochastic motion of finite-size immiscible impurities in a dilute quantum fluid at finite temperature

TL;DR

This paper investigates the stochastic motion of finite-size, immiscible impurities in a dilute quantum fluid at finite temperature using numerical simulations, revealing thermalization and Ornstein-Uhlenbeck dynamics influenced by temperature-dependent friction.

Contribution

It introduces a classical impurity model within a quantum fluid, demonstrating stochastic behavior and thermalization consistent with an Ornstein-Uhlenbeck process at finite temperature.

Findings

Impurities thermalize with the fluid.

Impurity dynamics follow an Ornstein-Uhlenbeck process.

Friction increases with temperature.

Abstract

The dynamics of an active, finite-size and immiscible impurity in a dilute quantum fluid at finite temperature is characterized by means of numerical simulations of the projected Gross--Pitaevskii equation. The impurity is modeled as a localized repulsive potential and described with classical degrees of freedom. It is shown that impurities of different sizes thermalize with the fluid and undergo a stochastic dynamics compatible with an Ornstein--Uhlenbeck process at sufficiently large time-lags. The velocity correlation function and the displacement of the impurity are measured and an increment of the friction with temperature is observed. Such behavior is phenomenologically explained in a scenario where the impurity exchanges momentum with a dilute gas of thermal excitations, experiencing an Epstein drag.