Quasi-Classical Dynamics

Abstract

We study quantum particles in interaction with a force-carrying field, in the quasi-classical limit. This limit is characterized by the field having a very large number of excitations (it is therefore macroscopic), while the particles retain their quantum nature. We prove that the interacting microscopic dynamics converges, in the quasi-classical limit, to an effective dynamics where the field acts as a classical environment that drives the quantum particles.

arXiv commentaccepted in J. Eur. Math. Soc., 47 pages, pdfLaTex

References in corpus (14)

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Cited by in corpus (8)

• Landau-Pekar equations and quantum fluctuations for the dynamics of a strongly coupled polaron
• Derivation of the Landau-Pekar equations in a many-body mean-field limit
• Classical Dynamics Generated by Long-Range Interactions for Lattice Fermions and Quantum Spins
• Ground State Properties in the Quasi-Classical Regime
• Scaling limits of bosonic ground states, from many-body to nonlinear Schr{ö}dinger
• Bogoliubov Dynamics and Higher-order Corrections for the Regularized Nelson Model
• Complete ionization for a non-autonomous point interaction model in d = 2
• Microscopic Derivation of Time-dependent Point Interactions