Energy Transfer in Scattering by Rotating Potentials

TL;DR

This paper investigates quantum scattering in rotating potentials, establishing bounded kinetic energy, wave operator completeness, and energy transfer during collisions, advancing understanding of time-dependent quantum interactions.

Contribution

It provides new results on uniform boundedness, wave operator existence, and energy transfer in quantum scattering with rotating potentials, which were not previously well-understood.

Findings

Kinetic energy remains uniformly bounded over time.

Wave operators exist and are complete.

Quantitative analysis of energy transfer during collisions.

Abstract

Quantum mechanical scattering theory is studied for time-dependent Schroedinger operators, in particular for particles in a rotating potential. Under various assumptions about the decay rate at infinity we show uniform boundedness in time for the kinetic energy of scattering states, existence and completeness of wave operators, and existence of a conserved quantity under scattering. In a simple model we determine the energy transfered to a particle by a collision with a rotating blade.