Chaotic motion at the emergence of the time averaged energy decay

Abstract

A system plus environment conservative model is used to characterize the nonlinear dynamics when the time averaged energy for the system particle starts to decay. The system particle dynamics is regular for low values of the $N$ environment oscillators and becomes chaotic in the interval $13\le N\le15$, where the system time averaged energy starts to decay. To characterize the nonlinear motion we estimate the Lyapunov exponent (LE), determine the power spectrum and the Kaplan-Yorke dimension. For much larger values of $N$ the energy of the system particle is completely transferred to the environment and the corresponding LEs decrease. Numerical evidences show the connection between the variations of the {\it amplitude} of the particles energy time oscillation with the time averaged energy decay and trapped trajectories.Comment: 18 pages and 10 figure

Quantum energy and coherence exchange with discrete baths

“…For longer times, t t disc , energy shows a power-law decay for harmonic potential and an exponential decay for Morse potential. In classical conservative systems, power-law decays of the energy [25,26] and the recurrence times statistics are related to sticky motion and memory effects due to a dynamics close to local invariants. This suggests that non-Markovian effects could be expected for the quantum case considered here when power-law decays are observed.…”

“…Differently from most of the previous studies, the environment here is composed by a finite number N of uncoupled HOs, as studied recently for classical continuous systems [25,26] and maps [27]. In such cases we say to have a discrete or structured bath.…”

“…Some experiments in which the non-Markovian behavior arises due to the discreteness of the bath can be mentioned: high-Q microwave cavities, quantum optics in materials with a photonic band gap, output coupling from a Bose-Einstein condensate to create an atom laser [28][29][30][31][32] or the decoherence phenomenon [33][34][35][36]. From the classical point of view, in the context of finite baths with uncoupled HO, there are some works which analyze the effect of discrete (structured) baths on the system energy decay [9,25,26] and on ratchet transport [37,38]. The main result found is that finite baths may induce a non-Markovian dynamics on the system particle.…”

Stickiness in a bouncer model: A slowing mechanism for Fermi acceleration

“…If the system presents any periodic or quasiperiodic motion, besides chaos in its dynamics, the FTLE distribution can have a secondary peak in the region of very low value of the Lyapunov exponent. Such a secondary peak is interpreted as sticky orbits along the dynamics evolution [16,17] responsible for trapping the dynamics. The distributions for several FTLE are shown in Fig.…”

“…On the other hand, a nonpositive Lyapunov exponent indicates regularity and the dynamics can be in principle periodic or quasiperiodic. The Lyapunov exponents are defined as follows [15] (see, for example, [16] for applications in higher dimensional systems):…”