Microscopic Derivation of Time-dependent Point Interactions
Abstract
We study the dynamics of the three-dimensional polaron - a quantum particle coupled to bosonic fields - in the quasi-classical regime. In this case the fields are 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 by-product, 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 Schr\"{o}dinger operators with suitably rescaled regular potentials.
Cite
@article{arxiv.1904.11012,
title = {Microscopic Derivation of Time-dependent Point Interactions},
author = {R. Carlone and M. Correggi and M. Falconi and M. Olivieri},
journal= {arXiv preprint arXiv:1904.11012},
year = {2021}
}
Comments
minor revision, to appear in SIAM J. Math. Anal., pdfLaTex, 28 pages