Perturbation Theory for the Quantum Time-Evolution in Rotating Potentials

TL;DR

This paper investigates the quantum time-evolution of particles in rotating potentials, demonstrating that rapid rotation causes the evolution to converge to that of an averaged, rotationally invariant potential, using perturbation theory.

Contribution

It introduces a perturbation theory approach to analyze quantum dynamics in rotating potentials and proves convergence to an averaged potential in the rapid rotation limit.

Findings

Strong convergence of the propagator to the averaged potential solution

Existence of the propagator for time-dependent rotating potentials

Convergence holds in the limit of rapid rotation

Abstract

The quantum mechanical time-evolution is studied for a particle under the influence of an explicitly time-dependent rotating potential. We discuss the existence of the propagator and we show that in the limit of rapid rotation it converges strongly to the solution operator of the Schr\"odinger equation with the averaged rotational invariant potential.