Exact closed form analytical solutions for vibrating cavities

TL;DR

This paper presents a method to derive exact closed-form solutions for one-dimensional vibrating cavities, revealing their stability properties and energy growth behaviors across various parameters.

Contribution

It introduces a novel approach to obtain exact solutions for vibrating cavities with arbitrary parameters, advancing understanding of their dynamical properties.

Findings

Solutions valid for arbitrary frequencies, amplitudes, and time regions.

Exponential instability observed in a broad parameter range.

Power-like energy growth at marginal stability.

Abstract

For one-dimensional vibrating cavity systems appearing in the standard illustration of the dynamical Casimir effect, we propose an approach to the construction of exact closed-form solutions. As new results, we obtain solutions that are given for arbitrary frequencies, amplitudes and time regions. In a broad range of parameters, a vibrating cavity model exhibits the general property of exponential instability. Marginal behavior of the system manifests in a power-like growth of radiated energy.