Some Hamiltonian Models of Friction II
arXiv:1108.5545 · doi:10.1063/1.4757278
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.
28 pages
References in corpus (2)
Cited by in corpus (11)
- Emission of Cherenkov Radiation as a Mechanism for Hamiltonian Friction
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- Attractors of nonlinear Hamiltonian PDEs
- Hamiltonians representing equations of motion with damping due to friction
- On the theory of slowing down gracefully
- A Lower Bound on the Critical Momentum of an Impurity in a Bose-Einstein Condensate
- Fermi's Golden Rule and Scattering for Nonlinear Klein-Gordon Equations with Metastable States
- Ballistic Motion of a Tracer Particle Coupled to a Bose gas