Rotating Singular Perturbations of the Laplacian

TL;DR

This paper investigates quantum systems with rotating singular potentials, establishing their Hamiltonians, explicit propagators, and analyzing the behavior as the rotation speed becomes very large.

Contribution

It introduces a rigorous construction of Hamiltonians for quantum particles with rotating point and blade interactions, and studies their asymptotic dynamics at high angular velocities.

Findings

Existence of self-adjoint Hamiltonians for rotating singular potentials.

Explicit formulas for the unitary propagators of these systems.

Strong convergence of the propagator to a limiting unitary group as rotation speed increases.

Abstract

We study a system of a quantum particle interacting with a singular time-dependent uniformly rotating potential in 2 and 3 dimensions: in particular we consider an interaction with support on a point (rotating point interaction) and on a set of codimension 1 (rotating blade). We prove the existence of the Hamiltonians of such systems as suitable self-adjoint operators and we give an explicit expression for their unitary semigroups. Moreover we analyze the asymptotic limit of large angular velocity and we prove strong convergence of the time-dependent propagator to some one-parameter unitary group as (\omega \to \infty).