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arXiv · 1904.11012

Microscopic Derivation of Time-dependent Point Interactions

R. Carlone·M. Correggi·M. Falconi·M. Olivieri
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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.

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R. Carlone, M. Correggi, M. Falconi, M. Olivieri. 2019-04-24. Microscopic Derivation of Time-dependent Point Interactions. https://doi.org/10.1137/20m1381344

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