Derivation of the Landau-Pekar equations in a many-body mean-field limit

Abstract

We consider the Fröhlich Hamiltonian in a mean-field limit where many bosonic particles weakly couple to the quantized phonon field. For large particle number and suitably small coupling, we show that the dynamics of the system is approximately described by the Landau-Pekar equations. These describe a Bose-Einstein condensate interacting with a classical polarization field, whose dynamics is effected by the condensate, i.e., the back-reaction of the phonons that are created by the particles during the time evolution is of leading order.

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Cited by in corpus (6)

• Landau-Pekar equations and quantum fluctuations for the dynamics of a strongly coupled polaron
• Ground State Properties in the Quasi-Classical Regime
• Bogoliubov Dynamics and Higher-order Corrections for the Regularized Nelson Model
• Scaling limits of bosonic ground states, from many-body to nonlinear Schr{ö}dinger
• Polaron catastrophe within quantum acoustics
• Convergence of states for polaron models in the classical limit