Emergence of Time-Dependent Point Interactions in Polaron Models

Metadata

SIMA 53(4), 4657-4691 (2021)

The published version is available under subscription at SIAM epubs.

arXiv 1904.11012

The preprint in pdf is available at arXiv.org.

Bibtex

The bibtex entry for the article can be downloaded here.

Abstract

We study the dynamics of the three-dimensional Fröhlich polaron - a quantum particle coupled to a bosonic field - in the quasi-classical regime, i.e., when the field is very intense and the corresponding degrees of freedom can be treated semiclassically. We prove that in such a regime the effective dynamics for the quantum particles is approximated by the one generated by a time-dependent point interaction, i.e., a singular time-dependent perturbation of the Laplacian supported in a point. As a byproduct, we also show that the unitary dynamics of a time-dependent point interaction can be approximated in strong operator topology by the one generated by time-dependent Schrödinger operators with suitably rescaled regular potentials.