Parametric Resonance in a dissipative system á la Kronig-Penney

2018/12/01 by L. Ferrari, Ferrari, Loris
Physics and Astronomy · #70Hxx #Classical Physics (physics.class-ph) #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.1812.00189

openalex publication_date 2018/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The competition between parametric resonance (PR) and dissipation is studied in the damped Kronig-Penney model, with time-dependent dissipation rate gamma(t). In the classical case, it is shown that dissipation leaves just a finite number of PR-bands at most, suppressing those at higher frequencies. An analysis of the Lewis-Reisenfeld invariant I(q,p,rho) is performed, showing that, in the PR regime, the auxiliary function rho(t) can be chosen bounded or unbounded, depending on the initial conditions.

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