Effective mass of the polaron -- revisited

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.

22 pages

References in corpus (1)

• The translation Invariant Massive Nelson Model: II. The Continuous Spectrum Below the Two-boson Threshold

Cited by in corpus (8)

• The Polaron at Strong Coupling
• Effective mass of the Polaron: a lower bound
• The Fröhlich Polaron at Strong Coupling -- Part I: The Quantum Correction to the Classical Energy
• Optimal parabolic upper bound for the energy-momentum relation of a strongly coupled polaron
• On the global minimum of the energy-momentum relation for the polaron
• Polaron models with regular interactions at strong coupling
• A Lower Bound on the Critical Momentum of an Impurity in a Bose-Einstein Condensate
• Asymptotic series for low-energy excitations of the Fröhlich Polaron at strong coupling