zur Startseite

Rupert Frank

A non-linear adiabatic theorem for the one-dimensional Landau-Pekar system

Abstract:The Landau-Pekar equations are a system of two coupled non-linear equations that describe the effective motion of a strongly coupled electron and its polarization field. The two equations have different time scales. We show that, if the electron is initially in the ground state of the effective Schrodinger operator generated by the field, then it (almost) remains in the ground state up to times of order one on the slow time scale. In contrast to a linear adiabatic theorem, the mechanism of this non-linear result is dispersion.

The talk is based on joint work with Gang Zhou.