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Effective Dynamics of a Tracer Particle Interacting with an Ideal Bose Gas

Dirk-André Deckert, Jürg Martin Fröhlich, Peter Pickl +1 more

Communications in Mathematical PhysicsApr 7, 201413 citations

Ballistic Motion of a Tracer Particle Coupled to a Bose gas

Froehlich, Juerg, Zhou Gang

We study the motion of a heavy tracer particle weakly coupled to a dense 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 derive the effective dynamics of the tracer particle, which is described by a non-linear integro-differential equation with memory, and prove that if the initial speed of the tracer particle is below the speed of sound in the Bose gas the motion of the particle approaches an inertial motion at constant velocity at large times.We study the motion of a heavy tracer particle weakly coupled to a dense 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 derive the effective dynamics of the tracer particle, which is described by a non-linear integro-differential equation with memory, and prove that if the initial speed of the tracer particle is below the speed of sound in the Bose gas the motion of the particle approaches an inertial motion at constant velocity at large times.

arXiv:1302.0429Feb 2, 20130 citations

Excitations of Atomic Bose--Einstein Condensates

Mark Edwards

APSNov 1, 19960 citations

Hamiltonian Dynamics of a Particle Interacting with a Wave Field

Daniel Egli, Jürg Martin Fröhlich, Zhou Gang +2 more

We study the Hamiltonian equations of motion of a heavy tracer particle interacting with a dense weakly interacting Bose-Einstein condensate in the classical (mean-field) limit. Solutions describing ballistic subsonic motion of the particle through the condensate are constructed. We establish asymptotic stability of ballistic subsonic motion.

arXiv:1211.6154Communications in Partial Differential EquationsJun 24, 201310 citations

Dynamics of Bose-Einstein Condensates

Benjamin Schlein

arXiv:0704.0813New Trends in Mathematical PhysicsJan 1, 20097 citations

Some Hamiltonian models of friction

Jürg Martin Fröhlich, Zhou Gang, Avy Soffer

Mathematical results on a model describing the motion of a tracer particle through a non-interacting Bose-Einstein condensate are described. In the limit of a very dense gas and for a very large particle mass, the dynamics of the coupled system is determined by classical nonlinear 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. A more general class of models involving interacting Bose gases will be studied in forthcoming papers.Mathematical results on a model describing the motion of a tracer particle through a non-interacting Bose-Einstein condensate are described. In the limit of a very dense gas and for a very large particle mass, the dynamics of the coupled system is determined by classical nonlinear 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. A more general class of models involving interacting Bose gases will be studied in forthcoming papers.

arXiv:1011.1283Journal of Mathematical PhysicsAug 1, 201115 citations

Dynamics of a Tracer Particle Interacting with Excitations of a Bose–Einstein Condensate

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