1,446 research outputs found
Stochastic approach to diffusion inside the chaotic layer of a resonance
We model chaotic diffusion, in a symplectic 4D map by using the result of a
theorem that was developed for stochastically perturbed integrable Hamiltonian
systems. We explicitly consider a map defined by a free rotator (FR) coupled to
a standard map (SM). We focus in the diffusion process in the action, , of
the FR, obtaining a semi--numerical method to compute the diffusion
coefficient. We study two cases corresponding to a thick and a thin chaotic
layer in the SM phase space and we discuss a related conjecture stated in the
past. In the first case the numerically computed probability density function
for the action is well interpolated by the solution of a Fokker-Planck
(F-P) equation, whereas it presents a non--constant time delay respect to the
concomitant F-P solution in the second case suggesting the presence of an
anomalous diffusion time scale. The explicit calculation of a diffusion
coefficient for a 4D symplectic map can be useful to understand the slow
diffusion observed in Celestial Mechanics and Accelerator Physics.Comment: This is the author's version of a work that was submitted to Physical
Review E (http://pre.aps.org
Quantum Integrals of Motion for Variable Quadratic Hamiltonians
We construct the integrals of motion for several models of the quantum damped
oscillators in nonrelativistic quantum mechanics in a framework of a general
approach to the time-dependent Schroedinger equation with variable quadratic
Hamiltonians. An extension of Lewis-Riesenfeld dynamical invariant is given.
The time-evolution of the expectation values of the energy related positive
operators is determined for the oscillators under consideration. A proof of
uniqueness of the corresponding Cauchy initial value problem is discussed as an
application.Comment: 32 pages, no figure
Wave propagation in one-dimensional nonlinear acoustic metamaterials
The propagation of waves in the nonlinear acoustic metamaterials (NAMs) is
fundamentally different from that in the conventional linear ones. In this
article we consider two one-dimensional NAM systems featuring respectively a
diatomic and a tetratomic meta unit-cell. We investigate the attenuation of the
wave, the band structure and the bifurcations to demonstrate novel nonlinear
effects, which can significantly expand the bandwidth for elastic wave
suppression and cause nonlinear wave phenomena. Harmonic averaging approach,
continuation algorithm, Lyapunov exponents are combined to study the frequency
responses, the nonlinear modes, bifurcations of periodic solutions and chaos.
The nonlinear resonances are studied and the influence of damping on
hyper-chaotic attractors is evaluated. Moreover, a "quantum" behavior is found
between the low-energy and high-energy orbits. This work provides an important
theoretical base for the further understandings and applications of NAMs
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