Persistence of the spectral gap for the Landau-Pekar equations

The Landau-Pekar equations describe the dynamics of a strongly coupled polaron. Here, we provide a class of initial data for which the associated effective Hamiltonian has a uniform spectral gap for all times. For such initial data, this allows us to extend the results on the adiabatic theorem for the Landau-Pekar equations and their derivation from the Frohlich model obtained in previous works to larger times.

Automated summary

By providing a class of specific initial data, the Landau-Pekar equations exhibit a uniform spectral gap for all times, allowing for the extension of results on the adiabatic theorem to larger time scales.