Some Hamiltonian Models of Friction

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.

19 Pages, 1 figure

References in corpus (1)

• The Excitation Spectrum for Weakly Interacting Bosons

Cited by in corpus (9)

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• Quantum dynamics of Bose-polaron in a $d$-dimensional Bose Einstein condensate
• Friction in a Model of Hamiltonian Dynamics
• Some Hamiltonian Models of Friction II
• Hamiltonian dynamics of a particle interacting with a wave field
• The effective mass problem for the Landau-Pekar equations
• Fluctuations in a kinetic transport model for quantum friction
• On the theory of slowing down gracefully
• A Lower Bound on the Critical Momentum of an Impurity in a Bose-Einstein Condensate