Derivation of an effective evolution equation for a strongly coupled polaron

Abstract

Fröhlich's polaron Hamiltonian describes an electron coupled to the quantized phonon field of an ionic crystal. We show that in the strong coupling limit the dynamics of the polaron is approximated by an effective non-linear partial differential equation due to Landau and Pekar, in which the phonon field is treated as a classical field.

46 pages

References in corpus (3)

• Classical limit of the Nelson model with cut off
• Dynamics of a strongly coupled polaron
• Wigner measures approach to the classical limit of the Nelson model: Convergence of dynamics and ground state energy

Cited by in corpus (17)

• On the dynamics of polarons in the strong-coupling limit
• Effective Potentials Generated by Field Interaction in the Quasi-Classical Limit
• The Landau-Pekar equations: Adiabatic theorem and accuracy
• Landau-Pekar equations and quantum fluctuations for the dynamics of a strongly coupled polaron
• Derivation of the Maxwell-Schrödinger Equations from the Pauli-Fierz Hamiltonian
• The Polaron at Strong Coupling
• Derivation of the Landau-Pekar equations in a many-body mean-field limit
• A note on the Fröhlich dynamics in the strong coupling limit
• Mean-field Dynamics for the Nelson Model with Fermions
• Persistence of the spectral gap for the Landau-Pekar equations
• 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
• Adiabatic approximation for the motion of Ginzburg-Landau vortex filament
• Effective Polaron Dynamics of an Impurity Particle Interacting with a Fermi Gas