On the dynamics of polarons in the strong-coupling limit

Abstract

The polaron model of H. Fröhlich describes an electron coupled to the quantized longitudinal optical modes of a polar crystal. In the strong-coupling limit one expects that the phonon modes may be treated classically, which leads to a coupled Schrödinger-Poisson system with memory. For the effective dynamics of the electron this amounts to a nonlinear and non-local Schrödinger equation. We use the Dirac-Frenkel variational principle to derive the Schrödinger-Poisson system from the Fröhlich model and we present new results on the accuracy of their solutions for describing the motion of Fröhlich polarons in the strong-coupling limit. Our main result extends to $N$-polaron systems.

21 pages

References in corpus (1)

• Geometric methods for nonlinear many-body quantum systems

Cited by in corpus (15)

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• The Landau-Pekar equations: Adiabatic theorem and accuracy
• Landau-Pekar equations and quantum fluctuations for the dynamics of a strongly coupled polaron
• The Polaron at Strong Coupling
• Derivation of the Landau-Pekar equations in a many-body mean-field limit
• Mean-field Dynamics for the Nelson Model with Fermions
• A note on the Fröhlich dynamics in the strong coupling limit
• Ground State Properties in the Quasi-Classical Regime
• Optimal parabolic upper bound for the energy-momentum relation of a strongly coupled polaron
• Mean-field limits of particles in interaction with quantized radiation fields
• The effective mass problem for the Landau-Pekar equations
• Bogoliubov Dynamics and Higher-order Corrections for the Regularized Nelson Model
• Microscopic Derivation of Time-dependent Point Interactions
• Polaron catastrophe within quantum acoustics