Theory of circle maps and the problem of one-dimensional optical resonator with a periodically moving wall

1998/10/09 by Rafael de la Llave, R. de la Llave, N. Petrov +1 · 3 citations
Computer Science · Mathematics · Physics and Astronomy · #Mechanical and Optical Resonators #Nonlinear Dynamics and Pattern Formation #Quantum Electrodynamics and Casimir Effect #chao-dyn #math-ph #math.MP #nlin.CD #physics.optics

paper · pdf · doi:10.1103/physreve.59.6637

published as Phys. Rev. E 59:6 (1999) 6637-6651 · 34 pages LaTeX (revtex) with eps figures, PACS: 02.30.Jr, 42.15.-i, 42.60.Da, 42.65.Yj

arxiv created 1998/10/09 · openalex publication_date 1999/06/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the electromagnetic field in a cavity with a periodically oscillating perfectly reflecting boundary and show that the mathematical theory of circle maps leads to several physical predictions. Notably, well-known results in the theory of circle maps (which we review briefly) imply that there are intervals of parameters where the waves in the cavity get concentrated in wave packets whose energy grows exponentially. Even if these intervals are dense for typical motions of the reflecting boundary, in the complement there is a positive measure set of parameters where the energy remains bounded.

Citations

• Zur Elektrodynamik bewegter Körper
• Effective Hamiltonian for the radiation in a cavity with a moving mirror and a time-varying dielectric medium

Cited by

• Exact closed-form analytical solutions for vibrating cavities
• The dynamical Casimir effect in a periodically changing domain: a dynamical systems approach
• Photon generation from vacuum in nondegenerate cavities with regular and random periodic displacements of boundaries