Do you want to publish a course? Click here

Characteristics of the Wave Function of Coupled Oscillators in Semiquantum Chaos

143   0   0.0 ( 0 )
 Added by Gang Wu
 Publication date 2007
  fields Physics
and research's language is English




Ask ChatGPT about the research

Using the method of adiabatic invariants and the Born-Oppenheimer approximation, we have successfully got the excited-state wave functions for a pair of coupled oscillators in the so-called textit{semiquantum chaos}. Some interesting characteristics in the textit{Fourier spectra} of the wave functions and its textit{Correlation Functions} in the regular and chaos states have been found, which offers a new way to distinguish the regular and chaotic states in quantum system.



rate research

Read More

The chaotic nature of a storage-ring Free Electron Laser (FEL) is investigated. The derivation of a low embedding dimension for the dynamics allows the low-dimensionality of this complex system to be observed, whereas its unpredictability is demonstrated, in some ranges of parameters, by a positive Lyapounov exponent. The route to chaos is then explored by tuning a single control parameter, and a period-doubling cascade is evidenced, as well as intermittence.
We numerically investigate the characteristics of chaos evolution during wave packet spreading in two typical one-dimensional nonlinear disordered lattices: the Klein-Gordon system and the discrete nonlinear Schr{o}dinger equation model. Completing previous investigations cite{SGF13} we verify that chaotic dynamics is slowing down both for the so-called `weak and `strong chaos dynamical regimes encountered in these systems, without showing any signs of a crossover to regular dynamics. The value of the finite-time maximum Lyapunov exponent $Lambda$ decays in time $t$ as $Lambda propto t^{alpha_{Lambda}}$, with $alpha_{Lambda}$ being different from the $alpha_{Lambda}=-1$ value observed in cases of regular motion. In particular, $alpha_{Lambda}approx -0.25$ (weak chaos) and $alpha_{Lambda}approx -0.3$ (strong chaos) for both models, indicating the dynamical differences of the two regimes and the generality of the underlying chaotic mechanisms. The spatiotemporal evolution of the deviation vector associated with $Lambda$ reveals the meandering of chaotic seeds inside the wave packet, which is needed for obtaining the chaotization of the lattices excited part.
We show that two coupled map lattices that are mutually coupled to one another with a delay can display zero delay synchronization if they are driven by a third coupled map lattice. We analytically estimate the parametric regimes that lead to synchronization and show that the presence of mutual delays enhances synchronization to some extent. The zero delay or isochronal synchronization is reasonably robust against mismatches in the internal parameters of the coupled map lattices and we analytically estimate the synchronization error bounds.
We explore the coherent dynamics in a small network of three coupled parametric oscillators and demonstrate the effect of frustration on the persistent beating between them. Since a single-mode parametric oscillator represents an analog of a classical Ising spin, networks of coupled parametric oscillators are considered as simulators of Ising spin models, aiming to efficiently calculate the ground state of an Ising network - a computationally hard problem. However, the coherent dynamics of coupled parametric oscillators can be considerably richer than that of Ising spins, depending on the nature of the coupling between them (energy preserving or dissipative), as was recently shown for two coupled parametric oscillators. In particular, when the energy-preserving coupling is dominant, the system displays everlasting coherent beats, transcending the Ising description. Here, we extend these findings to three coupled parametric oscillators, focusing in particular on the effect of frustration of the dissipative coupling. We theoretically analyze the dynamics using coupled nonlinear Mathieus equations, and corroborate our theoretical findings by a numerical simulation that closely mimics the dynamics of the system in an actual experiment. Our main finding is that frustration drastically modifies the dynamics. While in the absence of frustration the system is analogous to the two-oscillator case, frustration reverses the role of the coupling completely, and beats are found for small energy-preserving couplings.
A feasible model is introduced that manifests phenomena intrinsic to iterative complex analytic maps (such as the Mandelbrot set and Julia sets). The system is composed of two coupled alternately excited oscillators (or self-sustained oscillators). The idea is based on a turn-by-turn transfer of the excitation from one subsystem to another (S.P.~Kuznetsov, Phys.~Rev.~Lett. bf 95 rm, 2005, 144101) accompanied with appropriate nonlinear transformation of the complex amplitude of the oscillations in the course of the process. Analytic and numerical studies are performed. Special attention is paid to an analysis of the violation of the applicability of the slow amplitude method with the decrease in the ratio of the period of the excitation transfer to the basic period of the oscillations. The main effect is the rotation of the Mandelbrot-like set in the complex parameter plane; one more effect is the destruction of subtle small-scale fractal structure of the set due to the presence of non-analytic terms in the complex amplitude equations.
comments
Fetching comments Fetching comments
Sign in to be able to follow your search criteria
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا