Search results for "Periodic function"
showing 10 items of 41 documents
Floquet spectrum for two-level systems in quasiperiodic time-dependent fields
1992
We study the time evolution ofN-level quantum systems under quasiperiodic time-dependent perturbations. The problem is formulated in terms of the spectral properties of a quasienergy operator defined in an enlarged Hilbert space, or equivalently of a generalized Floquet operator. We discuss criteria for the appearance of pure point as well as continuous spectrum, corresponding respectively to stable quasiperiodic dynamics and to unstable chaotic behavior. We discuss two types of mechanisms that lead to instability. The first one is due to near resonances, while the second one is of topological nature and can be present for arbitrary ratios between the frequencies of the perturbation. We tre…
Noncommutative space and the low-energy physics of quasicrystals
2008
We prove that the effective low-energy, nonlinear Schroedinger equation for a particle in the presence of a quasiperiodic potential is the potential-free, nonlinear Schroedinger equation on noncommutative space. Thus quasiperiodicity of the potential can be traded for space noncommutativity when describing the envelope wave of the initial quasiperiodic wave.
Modified post-bifurcation dynamics and routes to chaos from double-Hopf bifurcations in a hyperchaotic system
2012
In order to understand the onset of hyperchaotic behavior recently observed in many systems, we study bifurcations in the modified Chen system leading from simple dynamics into chaotic regimes. In particular, we demonstrate that the existence of only one fixed point of the system in all regions of parameter space implies that this simple point attractor may only be destabilized via a Hopf or double Hopf bifurcation as system parameters are varied. Saddle-node, transcritical and pitchfork bifurcations are precluded. The normal form immediately following double Hopf bifurcations is constructed analytically by the method of multiple scales. Analysis of this generalized double Hopf normal form …
Noise Induced Phenomena in point Josephson junctions
2008
We present the analysis of the mean switching time and its standard deviation of short overdamped Josephson junctions, driven by a direct current and a periodic signal. The effect of noise enhanced stability is investigated. It is shown that fluctuations may both decrease and increase the switching time.
Analytical Study of the Thermal Induced Oscillations Known as Heartbeats
1998
Abstract A laser beam traveling horizontally at a short distance below the free surface of an absorbing solution exhibits various oscillatory states (periodic, quasiperiodic, and chaotic) which depend on both the buoyancy (Archimedes force) and the thermal coefficient of the surface tension (Marangoni effect). The beam oscillations have been called “heartbeats.” In this work, the heartbeats were produced by pumping 1-(2-pyridylazo)-2-naphthol (PAN) solutions in silicone oil with an Ar+continuous-wave laser beam. The relationships between PAN concentration and the other parameters that control the oscillatory behavior were studied. The frequency of the oscillations sensitively varied with sm…
Parametric conversion in micrometer and sub-micrometer structured ferroelectric crystals by surface poling
2012
We report on recent technological improvements concerning nonlinear patterning of lithium niobate and lithium tantalate in the micrometer and submicrometer scales using surface periodic poling for ferroelectric domain inversion. The fabricated samples were employed for frequency doubling via quasiphase-matching both in bulk and guided wave geometries, including forward and backward configurations and wavelength conversion in bands C and L. We also investigated short-period quasiperiodic samples with randomly distributed mark-to-space ratios.
Hidden Strange Nonchaotic Attractors
2021
In this paper, it is found numerically that the previously found hidden chaotic attractors of the Rabinovich–Fabrikant system actually present the characteristics of strange nonchaotic attractors. For a range of the bifurcation parameter, the hidden attractor is manifestly fractal with aperiodic dynamics, and even the finite-time largest Lyapunov exponent, a measure of trajectory separation with nearby initial conditions, is negative. To verify these characteristics numerically, the finite-time Lyapunov exponents, ‘0-1’ test, power spectra density, and recurrence plot are used. Beside the considered hidden strange nonchaotic attractor, a self-excited chaotic attractor and a quasiperiodic at…
KAM Techniques for Time Dependent Quantum Systems
1995
We consider a spin 1/2 in constant magnetic field perturbed by a quasiperiodic time dependent magnetic field. We discuss its stability properties in terms of the spectrum of the corresponding quasienergy operator. Since the spectrum of the unperturbed problem is dense, there appear small denominators in the perturbation theory, corresponding to resonances. They are treated with a technique developped by L.H. Eliasson, based on a KAM iteration.
Stochastic resonance in a tunnel diode.
1994
We study stochastic resonance in a fast bistable electronic system: a tunnel diode. We investigate the phenomenon in a higher frequency regime than that studied in previous experiments. Detailed measurements of the output signal are reported for two values of the frequency of the periodic signal: ${\mathit{f}}_{\mathit{s}}$=1 kHz and ${\mathit{f}}_{\mathit{s}}$=10 kHz. We observe, in one case (${\mathit{f}}_{\mathit{s}}$=1 kHz), a nonmonotonic behavior characterized by a sharp dip in the output noise level measured at the frequency of the driving signal.
Mixed Circular Convolutions and Zak Transforms
2014
In this chapter the notion of mixed circular convolution is introduced. The polynomial and discrete periodic splines defined on uniform grids are special cases of such convolutions. The so-called Zak transforms provide tools to handle mixed circular convolutions