THE LANDAU-PEKAR EQUATIONS: ADIABATIC THEOREM AND ACCURACY

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 Frohlich 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).

Automated summary

An adiabatic theorem is proved for the Landau-Pekar equations, allowing the derivation of new results on their accuracy as effective equations for time evolution generated by the Frohlich Hamiltonian with a large coupling constant alpha. It is shown that the time evolution of Pekar product states under coherent phonon fields, with the electron trapped by the phonons, is well approximated by the Landau-Pekar equations until times shorter than alpha squared.