Some Hamiltonian Models of Friction

TL;DR

This paper analyzes Hamiltonian models of a tracer particle moving through a Bose-Einstein condensate, demonstrating how classical non-linear equations describe friction-like deceleration due to Cerenkov radiation emission.

Contribution

It introduces a Hamiltonian framework for modeling friction in Bose-Einstein condensates, connecting quantum emission phenomena with classical dynamics.

Findings

Particle experiences deceleration due to Cerenkov radiation

Dynamics governed by classical non-linear Hamiltonian equations

Results applicable in dense, weakly interacting Bose gases

Abstract

Mathematical results on some models describing the motion of a tracer particle through a Bose-Einstein condensate are described. In the limit of a very dense, very weakly interacting Bose gas and for a very large particle mass, the dynamics of the coupled system is determined by classical non-linear Hamiltonian equations of motion. The particle's motion exhibits deceleration corresponding to friction (with memory) caused by the emission of Cerenkov radiation of gapless modes into the gas. Precise results are stated and outlines of proofs are presented. Some technical details are deferred to forthcoming papers.