Microscopic Derivation of Time-dependent Point Interactions

  title={Microscopic Derivation of Time-dependent Point Interactions},
  author={Raffaele Carlone and Michele Correggi and Marco Falconi and Marco Olivieri},
  journal={arXiv: Mathematical Physics},
We study the dynamics of the three-dimensional Frohlich 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… 
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