Some Hamiltonian Models of Friction II

TL;DR

This paper models the deceleration of a heavy tracer particle in a dense Bose gas due to Cerenkov radiation, proving decay properties of the system without assuming weak coupling, using dispersive estimates.

Contribution

It extends previous models by analyzing a non-weak coupling regime with dispersive estimates, showing the particle's deceleration and eventual rest.

Findings

Tracer particle decelerates and stops in the medium.

Friction arises from emission of Cerenkov radiation.

Decay properties of the system are mathematically proven.

Abstract

In the present paper we consider the motion of a very heavy tracer particle in a medium of a very dense, non-interacting Bose gas. We prove that, in a certain mean-field limit, the tracer particle will be decelerated and come to rest somewhere in the medium. Friction is caused by emission of Cerenkov radiation of gapless modes into the gas. Mathematically, a system of semilinear integro-differential equations, introduced in [FSSG10], describing a tracer particle in a dispersive medium is investigated, and decay properties of the solution are proven. This work is an extension of [FGS10]; it is an extension because no weak coupling limit for the interaction between tracer particle and medium is assumed. The technical methods used are dispersive estimates and a contraction principle.