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