On the theory of slowing down gracefully

TL;DR

This paper models how a heavy tracer particle slows down in a Bose-Einstein condensate due to emission of gapless modes, illustrating a form of Hamiltonian friction and its relation to decoherence.

Contribution

It provides a rigorous analysis of particle deceleration in a Bose gas within the mean-field limit, connecting classical Hamiltonian dynamics with quantum decoherence phenomena.

Findings

Particle is decelerated by emission of gapless modes (Cerenkov radiation).

In an ideal gas, the particle eventually stops.

In an interacting gas, the particle slows to the speed of Goldstone modes.

Abstract

We discuss the transport of a tracer particle through the Bose Einstein condensate of a Bose gas. The particle interacts with the atoms in the Bose gas through two-body interactions. In the limiting regime where the particle is very heavy and the Bose gas is very dense, but very weakly interacting ("mean-field limit"), the dynamics of this system corresponds to classical Hamiltonian dynamics. We show that, in this limit, the particle is decelerated by emission of gapless modes into the condensate (Cerenkov radiation). For an ideal gas, the particle eventually comes to rest. In an interacting Bose gas, the particle is decelerated until its speed equals the propagation speed of the Goldstone modes of the condensate. This is a model of "Hamiltonian friction". It is also of interest in connection with the phenomenon of "decoherence" in quantum mechanics. It is based on work we have carried out in collaboration with D Egli, IM Sigal and A Soffer.