title: Dissipative dynamics in a finite chaotic environment: Relationship between damping rate and Lyapunov exponent.
abstract: We consider the energy flow between a classical one-dimensional harmonic oscillator and a set of N two-dimensional chaotic oscillators, which represents the finite environment. Using linear response theory we obtain an analytical effective equation for the system harmonic oscillator, which includes a frequency dependent dissipation, a shift, and memory effects. The damping rate is expressed in terms of the environment mean Lyapunov exponent. A good agreement is shown by comparing theoretical and numerical results, even for environments with mixed (regular and chaotic) motion. Resonance between system and environment frequencies is shown to be more efficient to generate dissipation than larger mean Lyapunov exponents or a larger number of bath chaotic oscillators.
authors.affiliation: Departamento de Física, Universidade Federal do Paraná, 81531-980 Curitiba, Brazil.|Institut für Theoretische Physik, Technische Universität Dresden, D-01069 Dresden, Germany.
authors.forename: J C
authors.initials: JC
authors.lastname: Xavier
authors.affiliation: Institut für Theoretische Physik, Technische Universität Dresden, D-01069 Dresden, Germany.
authors.forename: W T
authors.initials: WT
authors.lastname: Strunz
authors.affiliation: Departamento de Física, Universidade Federal do Paraná, 81531-980 Curitiba, Brazil.|Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, D-01187 Dresden, Germany.
authors.forename: M W
authors.initials: MW
authors.lastname: Beims