The Landau-Pekar equations: Adiabatic theorem and accuracy

Abstract

We prove an adiabatic theorem for the Landau-Pekar equations. This allows us to derive new results on the accuracy of their use as effective equations for the time evolution generated by the Fröhlich Hamiltonian with large coupling constant $\alpha$. In particular, we show that the time evolution of Pekar product states with coherent phonon field and the electron being trapped by the phonons is well approximated by the Landau-Pekar equations until times short compared to ${\alpha }^2$.

improved error estimates in the adiabatic theorem (Theorem II.1), updated Remark II.4, to appear in Anal. PDE

References in corpus (4)

• Classical limit of the Nelson model with cut off
• Divergence of the effective mass of a polaron in the strong coupling limit
• A note on the Fröhlich dynamics in the strong coupling limit
• Persistence of the spectral gap for the Landau-Pekar equations

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
• Quasi-Classical Dynamics
• The effective mass problem for the Landau-Pekar equations
• 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
• A non-linear adiabatic theorem for the one-dimensional Landau-Pekar equations
• Convergence of states for polaron models in the classical limit