• DOI:10.1137/20M1381344
• Corpus ID: 131775262

Microscopic Derivation of Time-dependent Point Interactions

@article{Carlone2019MicroscopicDO,
  title={Microscopic Derivation of Time-dependent Point Interactions},
  author={Raffaele Carlone and Michele Correggi and Marco Falconi and Marco Olivieri},
  journal={arXiv: Mathematical Physics},
  year={2019}
}

• R. Carlone, M. Correggi, +1 author Marco Olivieri
• Published 24 April 2019
• Physics, Mathematics
• 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 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 Schrodinger operators with suitably rescaled regular potentials.