Microscopic Derivation of Timedependent Point Interactions
Abstract
We study the dynamics of the threedimensional polaron  a quantum particle coupled to bosonic fields  in the quasiclassical 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 timedependent point interaction, i.e., a singular timedependent perturbation of the Laplacian supported in a point. As a byproduct, we also show that the unitary dynamics of a timedependent point interaction can be approximated in strong operator topology by the one generated by timedependent Schrödinger operators with suitably rescaled regular potentials.
 Publication:

arXiv eprints
 Pub Date:
 April 2019
 arXiv:
 arXiv:1904.11012
 Bibcode:
 2019arXiv190411012C
 Keywords:

 Mathematical Physics
 EPrint:
 minor revision, to appear in SIAM J. Math. Anal., pdfLaTex, 28 pages