Superdiffusion in the Dissipative Standard Map

We consider transport properties of the chaotic (strange) attractor along unfolded trajectories of the dissipative standard map. It is shown that the diffusion process is normal except of the cases when a control parameter is close to some special values that correspond to the ballistic mode dynamics. Diffusion near the related crisises is anomalous and non-uniform in time: there are large time intervals during which the transport is normal or ballistic, or even superballistic. The anomalous superdiffusion seems to be caused by stickiness of trajectories to a non-chaotic and nowhere dense invariant Cantor set that plays a similar role as cantori in Hamiltonian chaos. We provide a numerical example of such a sticky set. Distribution function on the sticky set almost coincides with the distribution function (SRB measure) of the chaotic attractor.Comment: 10 Figure

Dynamics of the Chain of Oscillators with Long-Range Interaction: From Synchronization to Chaos

We consider a chain of nonlinear oscillators with long-range interaction of the type 1/l^{1+alpha}, where l is a distance between oscillators and 0< alpha <2. In the continues limit the system's dynamics is described by the Ginzburg-Landau equation with complex coefficients. Such a system has a new parameter alpha that is responsible for the complexity of the medium and that strongly influences possible regimes of the dynamics. We study different spatial-temporal patterns of the dynamics depending on alpha and show transitions from synchronization of the motion to broad-spectrum oscillations and to chaos.Comment: 22 pages, 10 figure

Maximal width of the separatrix chaotic layer

The main goal of the paper is to find the {\it absolute maximum} of the width of the separatrix chaotic layer as function of the frequency of the time-periodic perturbation of a one-dimensional Hamiltonian system possessing a separatrix, which is one of the major unsolved problems in the theory of separatrix chaos. For a given small amplitude of the perturbation, the width is shown to possess sharp peaks in the range from logarithmically small to moderate frequencies. These peaks are universal, being the consequence of the involvement of the nonlinear resonance dynamics into the separatrix chaotic motion. Developing further the approach introduced in the recent paper by Soskin et al. ({\it PRE} {\bf 77}, 036221 (2008)), we derive leading-order asymptotic expressions for the shape of the low-frequency peaks. The maxima of the peaks, including in particular the {\it absolute maximum} of the width, are proportional to the perturbation amplitude times either a logarithmically large factor or a numerical, still typically large, factor, depending on the type of system. Thus, our theory predicts that the maximal width of the chaotic layer may be much larger than that predicted by former theories. The theory is verified in simulations. An application to the facilitation of global chaos onset is discussed.Comment: 18 pages, 16 figures, submitted to PR

Finite Element Analysis of Strain Effects on Electronic and Transport Properties in Quantum Dots and Wires

Lattice mismatch in layered semiconductor structures with submicron length scales leads to extremely high nonuniform strains. This paper presents a finite element technique for incorporating the effects of the nonuniform strain into an analysis of the electronic properties of SiGe quantum structures. Strain fields are calculated using a standard structural mechanics finite element package and the effects are included as a nonuniform potential directly in the time independent Schrodinger equation; a k-p Hamiltonian is used to model the effects of multiple valence subband coupling. A variational statement of the equation is formulated and solved using the finite element method. This technique is applied to resonant tunneling diode quantum dots and wires; the resulting densities of states confined to the quantum well layers of the devices are compared to experimental current-voltage I(V) curves.Comment: 17 pages (LaTex), 18 figures (JPEG), submitted to Journal of Applied Physic

Dynamic instabilities in resonant tunneling induced by a magnetic field

We show that the addition of a magnetic field parallel to the current induces self sustained intrinsic current oscillations in an asymmetric double barrier structure. The oscillations are attributed to the nonlinear dynamic coupling of the current to the charge trapped in the well, and the effect of the external field over the local density of states across the system. Our results show that the system bifurcates as the field is increased, and may transit to chaos at large enough fields.Comment: 4 pages, 3 figures, accepted in Phys. Rev. Letter

Stochastic heating of a molecular nanomagnet

We study the excitation dynamics of a single molecular nanomagnet by static and pulsed magnetic fields. Based on a stability analysis of the classical magnetization dynamics we identify analytically the fields parameters for which the energy is stochastically pumped into the system in which case the magnetization undergoes diffusively and irreversibly a large angle deflection. An approximate analytical expression for the diffusion constant in terms of the fields parameters is given and assessed by full numerical calculations.Comment: 5 pages, 4 figures, to appear in Phys. Rev.

Web-assisted tunneling in the kicked harmonic oscillator

We show that heating of harmonically trapped ions by periodic delta kicks is dramatically enhanced at isolated values of the Lamb-Dicke parameter. At these values, quasienergy eigenstates localized on island structures undergo avoided crossings with extended web-states.Comment: 4 pages, 4 figures. Accepted for publication in Phys. Rev. Let

On the unconstrained expansion of a spherical plasma cloud turning collisionless : case of a cloud generated by a nanometer dust grain impact on an uncharged target in space

Nano and micro meter sized dust particles travelling through the heliosphere at several hundreds of km/s have been repeatedly detected by interplanetary spacecraft. When such fast moving dust particles hit a solid target in space, an expanding plasma cloud is formed through the vaporisation and ionisation of the dust particles itself and part of the target material at and near the impact point. Immediately after the impact the small and dense cloud is dominated by collisions and the expansion can be described by fluid equations. However, once the cloud has reached micro-m dimensions, the plasma may turn collisionless and a kinetic description is required to describe the subsequent expansion. In this paper we explore the late and possibly collisionless spherically symmetric unconstrained expansion of a single ionized ion-electron plasma using N-body simulations. Given the strong uncertainties concerning the early hydrodynamic expansion, we assume that at the time of the transition to the collisionless regime the cloud density and temperature are spatially uniform. We do also neglect the role of the ambient plasma. This is a reasonable assumption as long as the cloud density is substantially higher than the ambient plasma density. In the case of clouds generated by fast interplanetary dust grains hitting a solid target some 10^7 electrons and ions are liberated and the in vacuum approximation is acceptable up to meter order cloud dimensions. ..

Decoherence and the quantum-classical limit in the presence of chaos

We investigate how decoherence affects the short-time separation between quantum and classical dynamics for classically chaotic systems, within the framework of a specific model. For a wide range of parameters, the distance between the corresponding phase-space distributions depends on a single parameter $\chi$ that relates an effective Planck constant $\hbar_{\rm eff}$, the Lyapunov coeffficient, and the diffusion constant. This distance peaks at a time that depends logarithmically on $\hbar_{\rm eff}$, in agreement with previous estimations of the separation time for Hamiltonian systems. However, for $\chi\lesssim 1$, the separation remains small, going down with $\hbar_{\rm eff}^2$, so the concept of separation time loses its meaning.Comment: 5 pages, 4 figures (in 6 postscript files) two of them are color figure