Exact closed-form analytical solutions for vibrating cavities

2007/06/19 by Pawel Wegrzyn, Paweł Wegrzyn · 1 citation
Materials Science · Physics and Astronomy · #Mechanical and Optical Resonators #Nonlocal and gradient elasticity in micro/nano structures #Quantum Electrodynamics and Casimir Effect #quant-ph

paper · pdf · doi:10.1088/0953-4075/40/13/008

published as J. Phys. B: At. Mol. Opt. Phys. 40, 2621-2640 (2007) · 17 pages, 7 figures

openalex publication_date 2007/06/19 · arxiv created 2007/06/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Motion Induced Radiation from a Vibrating Cavity
• Theory of circle maps and the problem of one-dimensional optical resonator with a periodically moving wall
• A novel experimental approach for the detection of the dynamical Casimir effect
• Dynamical Casimir effect with Dirichlet and Neumann boundary conditions
• The Casimir effect: Recent controversies and progress
• Casimir interaction between two concentric cylinders: Exact versus semiclassical results
• Effective Hamiltonian for the radiation in a cavity with a moving mirror and a time-varying dielectric medium

Cited by

• The dynamical Casimir effect for two oscillating mirrors in 3D