Microscopic Derivation of Time-dependent Point Interactions

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 Schrödinger operators with suitably rescaled regular potentials.

minor revision, to appear in SIAM J. Math. Anal., pdfLaTex, 28 pages

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Cited by in corpus (6)

• Landau-Pekar equations and quantum fluctuations for the dynamics of a strongly coupled polaron
• Derivation of the Landau-Pekar equations in a many-body mean-field limit
• Ground State Properties in the Quasi-Classical Regime
• Quasi-Classical Dynamics
• Bogoliubov Dynamics and Higher-order Corrections for the Regularized Nelson Model
• Complete ionization for a non-autonomous point interaction model in d = 2