Emergence of Time-Dependent Point Interactions in Polaron Models


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

The published version is available under subscription at SIAM epubs.

arXiv 1904.11012

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The bibtex entry for the article can be downloaded here.


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.