Stochastic Motion of Finite-Size Immiscible Impurities in a Dilute Quantum Fluid at Finite Temperature

Abstract

In this work we aim at studying numerically the dynamics of an immiscible and finite-size impurity in a quantum fluid at finite temperature. Its dynamics is characterized by means of numerical simulations of the Fourier truncated 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.