Lower bound on the energy-momentum relation of the polaron

Steffen Polzer

Lower bound on the energy-momentum relation of the polaron

Mathematical Physics 2026-07-06 v1

Authors: Steffen Polzer

Abstract

For a class of polaron-type models, we establish a lower bound on the energy-momentum relation in terms of the vacuum overlap and the spectral gap of the total momentum zero Hamiltonian. We show convergence of the rescaled mean square displacement of the associated path measure to the inverse of the effective mass. We derive a probabilistic criterion for the absence of ground states at large total momentum.

Keywords

polaron energy-momentum relation vacuum overlap spectral gap effective mass ground state

Cite

@article{arxiv.2607.05286,
  title  = {Lower bound on the energy-momentum relation of the polaron},
  author = {Steffen Polzer},
  journal= {arXiv preprint arXiv:2607.05286},
  year   = {2026}
}