Ballistic Motion of a Tracer Particle Coupled to a Bose gas

TL;DR

This paper investigates the motion of a heavy tracer particle in a Bose-Einstein condensate, deriving an effective non-linear equation and showing inertial motion at low initial speeds.

Contribution

It derives a new effective non-linear integro-differential equation describing the tracer particle's dynamics in a Bose gas.

Findings

Particle approaches inertial motion at large times if initial speed is below sound speed.

Effective dynamics are governed by a non-linear integro-differential equation with memory.

Motion converges to constant velocity in the mean-field limit.

Abstract

We study the motion of a heavy tracer particle weakly coupled to a dense interacting Bose gas exhibiting Bose-Einstein condensation. In the so-called mean-field limit, the dynamics of this system approaches one determined by nonlinear Hamiltonian evolution equations. We derive the effective dynamics of the tracer particle, which is described by a non-linear integro-differential equation with memory, and prove that if the initial speed of the tracer particle is below the speed of sound in the Bose gas the motion of the particle approaches an inertial motion at constant velocity at large times.