Landau-Pekar equations and quantum fluctuations for the dynamics of a strongly coupled polaron

Abstract

We consider the Fröhlich Hamiltonian with large coupling constant $\alpha$. For initial data of Pekar product form with coherent phonon field and with the electron minimizing the corresponding energy, we provide a norm approximation of the evolution, valid up to times of order ${\alpha }^2$. The approximation is given in terms of a Pekar product state, evolved through the Landau-Pekar equations, corrected by a Bogoliubov dynamics taking quantum fluctuations into account. This allows us to show that the Landau-Pekar equations approximately describe the evolution of the electron- and one-phonon reduced density matrices under the Fröhlich dynamics up to times of order ${\alpha }^2$.

24 pages

References in corpus (3)

• Classical limit of the Nelson model with cut off
• Derivation of the Landau-Pekar equations in a many-body mean-field limit
• A note on the Fröhlich dynamics in the strong coupling limit

Cited by in corpus (9)

• A note on the Fröhlich dynamics in the strong coupling limit
• Optimal parabolic upper bound for the energy-momentum relation of a strongly coupled polaron
• Bogoliubov Dynamics and Higher-order Corrections for the Regularized Nelson Model
• The effective mass problem for the Landau-Pekar equations
• Polaron models with regular interactions at strong coupling
• Polaron catastrophe within quantum acoustics
• One-dimensional Fermi polaron after a kick: two-sided singularity of the momentum distribution, Bragg reflection and other exact results
• Ubiquity of bound states for the strongly coupled polaron
• Effective pair interaction between impurity particles induced by a dense Fermi gas