117 research outputs found
Separatrix chaos: new approach to the theoretical treatment
We develop a new approach to the theoretical treatment of the separatrix
chaos, using a special analysis of the separatrix map. The approach allows us
to describe boundaries of the separatrix chaotic layer in the Poincar\'{e}
section and transport within the layer. We show that the maximum which the
width of the layer in energy takes as the perturbation frequency varies is much
larger than the perturbation amplitude, in contrast to predictions by earlier
theories suggesting that the maximum width is of the order of the amplitude.
The approach has also allowed us to develop the self-consistent theory of the
earlier discovered (PRL 90, 174101 (2003)) drastic facilitation of the onset of
global chaos between adjacent separatrices. Simulations agree with the theory.Comment: 10 pages, 4 figures, proceedings of the conference "Chaos, Complexity
and Transport" (Marseille, 5-9 June 2007), in pres
New approach to the treatment of separatrix chaos and its application to the global chaos onset between adjacent separatrices
We have developed the {\it general method} for the description of {\it
separatrix chaos}, basing on the analysis of the separatrix map dynamics.
Matching it with the resonant Hamiltonian analysis, we show that, for a given
amplitude of perturbation, the maximum width of the chaotic layer in energy may
be much larger than it was assumed before. We apply the above theory to explain
the drastic facilitation of global chaos onset in time-periodically perturbed
Hamiltonian systems possessing two or more separatrices, previously discovered
(PRL 90, 174101 (2003)). The theory well agrees with simulations. We also
discuss generalizations and applications. Examples of applications of the
facilitation include: the increase of the DC conductivity in spatially periodic
structures, the reduction of activation barriers for noise-induced transitions
and the related acceleration of spatial diffusion, the facilitation of the
stochastic web formation in a wave-driven or kicked oscillator.Comment: 29 pages, 16 figures (figs. are of reduced quality, original files
are available on request from authors), paper has been significantly revised
and resubmitted to PR
Low Energy Properties of the Kondo chain in the RKKY regime
We study the Kondo chain in the regime of high spin concentration where the
low energy physics is dominated by the Ruderman-Kittel-Kasuya-Yosida (RKKY)
interaction. As has been recently shown (A. M. Tsvelik and O. M. Yevtushenko,
Phys. Rev. Lett 115, 216402 (2015)), this model has two phases with drastically
different transport properties depending on the anisotropy of the exchange
interaction. In particular, the helical symmetry of the fermions is
spontaneously broken when the anisotropy is of the easy plane type (EP). This
leads to a parametrical suppression of the localization effects. In the present
paper we substantially extend the previous theory, in particular, by analyzing
a competition of forward- and backward- scattering, including into the theory
short range electron interactions and calculating spin correlation functions.
We discuss applicability of our theory and possible experiments which could
support the theoretical findings.Comment: 24 pages, 8 figures, 5 appendice
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