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
. 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
.
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