160 research outputs found
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
A new approach to the treatment of Separatrix Chaos and its applications
We consider time-periodically perturbed 1D Hamiltonian systems possessing one or more separatrices. If the perturbation is weak, then the separatrix chaos is most developed when the perturbation frequency lies in the logarithmically small or moderate ranges: this corresponds to the involvement of resonance dynamics into the separatrix chaos. We develop a method matching the discrete chaotic dynamics of the separatrix map and the continuous regular dynamics of the resonance Hamiltonian. The method has allowed us to solve the long-standing problem of an accurate description of the maximum of the separatrix chaotic layer width as a function of the perturbation frequency. It has also allowed us to predict and describe
new phenomena including, in particular: (i) a drastic facilitation of the onset of global chaos between neighbouring separatrices, and (ii) a huge increase in the
size of the low-dimensional stochastic web
Drastic facilitation of the onset of global chaos in a periodically driven Hamiltonian system due to an extremum in the dependence of eigenfrequency on energy
The Chirikov resonance-overlap criterion predicts the onset of global chaos
if nonlinear resonances overlap in energy, which is conventionally assumed to
require a non-small magnitude of perturbation. We show that, for a
time-periodic perturbation, the onset of global chaos may occur at unusually
{\it small} magnitudes of perturbation if the unperturbed system possesses more
than one separatrix. The relevant scenario is the combination of the overlap in
the phase space between resonances of the same order and their overlap in
energy with chaotic layers associated with separatrices of the unperturbed
system. One of the most important manifestations of this effect is a drastic
increase of the energy range involved into the unbounded chaotic transport in
spatially periodic system driven by a rather {\it weak} time-periodic force,
provided the driving frequency approaches the extremal eigenfrequency or its
harmonics. We develop the asymptotic theory and verify it in simulations.Comment: 5 pages, 4 figures, LaTeX, to appear PR
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