Resonant transitions due to changing boundaries

TL;DR

This paper investigates how small, boundary-shape-preserving movements of a particle's confining box induce resonant transitions at natural frequencies, revealing effects on angular momentum and specific boundary change cases.

Contribution

It introduces the concept of resonant transitions caused by boundary movements without shape change and analyzes a special case of circular boundary deformation.

Findings

Resonant transitions occur at natural frequencies and depend on boundary velocity Fourier components.

Boundary movements do not affect the particle's angular momentum.

A detailed analysis of circular boundary changes highlights specific effects.

Abstract

The problem of a particle confined in a box with moving walls is studied, focusing on the case of small perturbations which do not alter the shape of the boundary (\lq pantography\rq). The presence of resonant transitions involving the natural transition frequencies of the system and the Fourier transform of the velocity of the walls of the box is brought to the light. The special case of a pantographic change of a circular box is analyzed in dept, also bringing to light the fact that the movement of the boundary cannot affect the angular momentum of the particle.