Abstract
Properties of the energy-momentum relation for the Fröhlich polaron are of
continuing interest, especially for large values of the coupling constant. By
combining spectral theory with the available results on the central limit
theorem for the polaron path measure we prove that, except for an intermediate
range of couplings, the inverse effective mass is strictly positive and
coincides with the diffusion constant. Such a result is established also for
polaron-type models with a suitable ultraviolet cut-off and for arbitrary
values of the coupling constant. We point out a slightly stronger variant of
the central limit theorem which would imply that the energy-momentum relation
has a unique global minimum attained at zero momentum.
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