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

Landau equations and asymptotic operation

The pinched/non-pinched classification of intersections of causal singularities of propagators in Minkowski space is reconsidered in the context of the theory of asymptotic operation as a first step towards extension of the latter to non-Euclidean asymptotic regimes. A highly visual distribution-theoretic technique of singular wave fronts is tailored to the needs of the theory of Feynman diagrams. Besides a simple derivation of the usual Landau equations in the case of the conventional singularities, the technique naturally extends to other types of singularities e.g. due to linear denominators in non-covariant gauges etc. As another application, the results of Euclidean asymptotic operation are extended to a class of quasi-Euclidean asymptotic regimes in Minkowski space.Comment: 15p PS (GSview), IJMP-A (accepted

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. ..

Space-Time Complexity in Hamiltonian Dynamics

New notions of the complexity function C(epsilon;t,s) and entropy function S(epsilon;t,s) are introduced to describe systems with nonzero or zero Lyapunov exponents or systems that exhibit strong intermittent behavior with ``flights'', trappings, weak mixing, etc. The important part of the new notions is the first appearance of epsilon-separation of initially close trajectories. The complexity function is similar to the propagator p(t0,x0;t,x) with a replacement of x by the natural lengths s of trajectories, and its introduction does not assume of the space-time independence in the process of evolution of the system. A special stress is done on the choice of variables and the replacement t by eta=ln(t), s by xi=ln(s) makes it possible to consider time-algebraic and space-algebraic complexity and some mixed cases. It is shown that for typical cases the entropy function S(epsilon;xi,eta) possesses invariants (alpha,beta) that describe the fractal dimensions of the space-time structures of trajectories. The invariants (alpha,beta) can be linked to the transport properties of the system, from one side, and to the Riemann invariants for simple waves, from the other side. This analog provides a new meaning for the transport exponent mu that can be considered as the speed of a Riemann wave in the log-phase space of the log-space-time variables. Some other applications of new notions are considered and numerical examples are presented.Comment: 27 pages, 6 figure

Giant acceleration in slow-fast space-periodic Hamiltonian systems

Motion of an ensemble of particles in a space-periodic potential well with a weak wave-like perturbation imposed is considered. We found that slow oscillations of wavenumber of the perturbation lead to occurrence of directed particle current. This current is amplifying with time due to giant acceleration of some particles. It is shown that giant acceleration is linked with the existence of resonant channels in phase space

The possibility of a metal insulator transition in antidot arrays induced by an external driving

It is shown that a family of models associated with the kicked Harper model is relevant for cyclotron resonance experiments in an antidot array. For this purpose a simplified model for electronic motion in a related model system in presence of a magnetic field and an AC electric field is developed. In the limit of strong magnetic field it reduces to a model similar to the kicked Harper model. This model is studied numerically and is found to be extremely sensitive to the strength of the electric field. In particular, as the strength of the electric field is varied a metal -- insulator transition may be found. The experimental conditions required for this transition are discussed.Comment: 6 files: kharp.tex, fig1.ps fig2.ps fi3.ps fig4.ps fig5.p

Quantized Orbits and Resonant Transport

A tight binding representation of the kicked Harper model is used to obtain an integrable semiclassical Hamiltonian consisting of degenerate "quantized" orbits. New orbits appear when renormalized Harper parameters cross integer multiples of $\pi/2$. Commensurability relations between the orbit frequencies are shown to correlate with the emergence of accelerator modes in the classical phase space of the original kicked problem. The signature of this resonant transport is seen in both classical and quantum behavior. An important feature of our analysis is the emergence of a natural scaling relating classical and quantum couplings which is necessary for establishing correspondence.Comment: REVTEX document - 8 pages + 3 postscript figures. Submitted to Phys.Rev.Let

Chaotic and pseudochaotic attractors of perturbed fractional oscillator

We consider a nonlinear oscillator with fractional derivative of the order alpha. Perturbed by a periodic force, the system exhibits chaotic motion called fractional chaotic attractor (FCA). The FCA is compared to the ``regular'' chaotic attractor. The properties of the FCA are discussed and the ``pseudochaotic'' case is demonstrated.Comment: 20 pages, 7 figure