Emission of Cherenkov Radiation as a Mechanism for Hamiltonian Friction

Abstract

We study the motion of a heavy tracer particle weakly coupled to a dense, weakly interacting Bose gas exhibiting Bose-Einstein condensation. In the so-called mean-field limit, the dynamics of this system approaches one determined by nonlinear Hamiltonian evolution equations. We prove that if the initial speed of the tracer particle is above the speed of sound in the Bose gas, and for a suitable class of initial states of the Bose gas, the particle decelerates due to emission of Cherenkov radiation of sound waves, and its motion approaches a uniform motion at the speed of sound, as time tends to infinity.

54 Pages, 2 figures, typos corrected, physical relevance discussed

Cited by in corpus (11)

• The Reality of Casimir Friction
• Quantum dynamics of Bose-polaron in a $d$-dimensional Bose Einstein condensate
• Attractors of Hamilton nonlinear partial differential equations
• The effective mass problem for the Landau-Pekar equations
• Free time evolution of a tracer particle coupled to a Fermi gas in the high-density limit
• Attractors of nonlinear Hamiltonian PDEs
• Radiation-induced instability of a finite-chord Nemtsov membrane
• A Lower Bound on the Critical Momentum of an Impurity in a Bose-Einstein Condensate
• Fermi's Golden Rule and $H^1$ Scattering for Nonlinear Klein-Gordon Equations with Metastable States
• Mean field dynamics of a quantum tracer particle interacting with a boson gas
• On global attractors and radiation damping for nonrelativistic particle coupled to scalar field