Dynamics of a particle confined in a two-dimensional dilating and deforming domain

TL;DR

This paper investigates the quantum dynamics of a particle in a two-dimensional box with moving and deforming boundaries, extending previous one-dimensional results to understand shape changes' effects on quantum behavior.

Contribution

It introduces a method to analyze a 2D quantum billiard with moving walls by transforming the problem into a fixed boundary framework, highlighting the impact of shape deformation.

Findings

Shape deformation significantly affects quantum particle behavior.

The mathematical approach effectively handles moving boundary problems in 2D.

Comparison shows differences between pantographic and deformed boundary cases.

Abstract

Some recent results concerning a particle confined in a one-dimensional box with moving walls are briefly reviewed. By exploiting the same techniques used for the 1D problem, we investigate the behavior of a quantum particle confined in a two-dimensional box (a 2D billiard) whose walls are moving, by recasting the relevant mathematical problem with moving boundaries in the form of a problem with fixed boundaries and time-dependent Hamiltonian. Changes of the shape of the box are shown to be important, as it clearly emerges from the comparison between the "pantographic", case (same shape of the box through all the process) and the case with deformation.