49 research outputs found
Destruction of Anderson localization in quantum nonlinear Schr\"odinger lattices
The four-wave interaction in quantum nonlinear Schr\"odinger lattices with
disorder is shown to destroy the Anderson localization of waves, giving rise to
unlimited spreading of the nonlinear field to large distances. Moreover, the
process is not thresholded in the quantum domain, contrary to its "classical"
counterpart, and leads to an accelerated spreading of the subdiffusive type,
with the dispersion for
. The results, presented here, shed new light on the
origin of subdiffusion in systems with a broad distribution of relaxation
times.Comment: 4 pages, no figure
A topological approximation of the nonlinear Anderson model
We study the phenomena of Anderson localization in the presence of nonlinear
interaction on a lattice. A class of nonlinear Schrodinger models with
arbitrary power nonlinearity is analyzed. We conceive the various regimes of
behavior, depending on the topology of resonance-overlap in phase space,
ranging from a fully developed chaos involving Levy flights to pseudochaotic
dynamics at the onset of delocalization. It is demonstrated that quadratic
nonlinearity plays a dynamically very distinguished role in that it is the only
type of power nonlinearity permitting an abrupt localization-delocalization
transition with unlimited spreading already at the delocalization border. We
describe this localization-delocalization transition as a percolation
transition on a Cayley tree. It is found in vicinity of the criticality that
the spreading of the wave field is subdiffusive in the limit
t\rightarrow+\infty. The second moment grows with time as a powerlaw t^\alpha,
with \alpha = 1/3. Also we find for superquadratic nonlinearity that the analog
pseudochaotic regime at the edge of chaos is self-controlling in that it has
feedback on the topology of the structure on which the transport processes
concentrate. Then the system automatically (without tuning of parameters)
develops its percolation point. We classify this type of behavior in terms of
self-organized criticality dynamics in Hilbert space. For subquadratic
nonlinearities, the behavior is shown to be sensitive to details of definition
of the nonlinear term. A transport model is proposed based on modified
nonlinearity, using the idea of stripes propagating the wave process to large
distances. Theoretical investigations, presented here, are the basis for
consistency analysis of the different localization-delocalization patterns in
systems with many coupled degrees of freedom in association with the asymptotic
properties of the transport.Comment: 20 pages, 2 figures; improved text with revisions; accepted for
publication in Physical Review
L\'evy flights on a comb and the plasma staircase
We formulate the problem of confined L\'evy flight on a comb. The comb
represents a sawtooth-like potential field , with the asymmetric teeth
favoring net transport in a preferred direction. The shape effect is modeled as
a power-law dependence within the sawtooth period,
followed by an abrupt drop-off to zero, after which the initial power-law
dependence is reset. It is found that the L\'evy flights will be confined in
the sense of generalized central limit theorem if (i) the spacing between the
teeth is sufficiently broad, and (ii) , where is the fractal
dimension of the flights. In particular, for the Cauchy flights (),
. The study is motivated by recent observations of
localization-delocalization of transport avalanches in banded flows in the Tore
Supra tokamak and is intended to devise a theory basis to explain the observed
phenomenology.Comment: 13 pages; 3 figures; accepted for publication in Physical Review
Fractional generalization of the Ginzburg-Landau equation: An unconventional approach to critical phenomena in complex media
Equations built on fractional derivatives prove to be a powerful tool in the
description of complex systems when the effects of singularity, fractal
supports, and long-range dependence play a role. In this paper, we advocate an
application of the fractional derivative formalism to a fairly general class of
critical phenomena when the organization of the system near the phase
transition point is influenced by a competing nonlocal ordering. Fractional
modifications of the free energy functional at criticality and of the widely
known Ginzburg-Landau equation central to the classical Landau theory of
second-type phase transitions are discussed in some detail. An implication of
the fractional Ginzburg-Landau equation is a renormalization of the transition
temperature owing to the nonlocality present.Comment: 10 pages, improved content, submitted for publication to Phys. Lett.
Self-similar transport processes in a two-dimensional realization of multiscale magnetic field turbulence
We present the results of a numerical investigation of charged-particle
transport across a synthesized magnetic configuration composed of a constant
homogeneous background field and a multiscale perturbation component simulating
an effect of turbulence on the microscopic particle dynamics. Our main goal is
to analyze the dispersion of ideal test particles faced to diverse conditions
in the turbulent domain. Depending on the amplitude of the background field and
the input test particle velocity, we observe distinct transport regimes ranging
from subdiffusion of guiding centers in the limit of Hamiltonian dynamics to
random walks on a percolating fractal array and further to nearly diffusive
behavior of the mean-square particle displacement versus time. In all cases, we
find complex microscopic structure of the particle motion revealing long-time
rests and trapping phenomena, sporadically interrupted by the phases of active
cross-field propagation reminiscent of Levy-walk statistics. These complex
features persist even when the particle dispersion is diffusive. An
interpretation of the results obtained is proposed in connection with the
fractional kinetics paradigm extending the microscopic properties of transport
far beyond the conventional picture of a Brownian random motion. A calculation
of the transport exponent for random walks on a fractal lattice is advocated
from topological arguments. An intriguing indication of the topological
approach is a gap in the transport exponent separating Hamiltonian-like and
fractal random walk-like dynamics, supported through the simulation.Comment: 10 pages (including cover page), 7 figures, improved content,
accepted for publication in Physica Script
Stretched exponential relaxation and ac universality in disordered dielectrics
This paper is concerned with the connection between the properties of
dielectric relaxation and ac (alternating-current) conduction in disordered
dielectrics. The discussion is divided between the classical linear-response
theory and a self-consistent dynamical modeling. The key issues are, stretched
exponential character of dielectric relaxation, power-law power spectral
density, and anomalous dependence of ac conduction coefficient on frequency. We
propose a self-consistent model of dielectric relaxation, in which the
relaxations are described by a stretched exponential decay function.
Mathematically, our study refers to the expanding area of fractional calculus
and we propose a systematic derivation of the fractional relaxation and
fractional diffusion equations from the property of ac universality.Comment: 8 pages, 2 figure
Common Therapeutic Factors in Psychotherapy and Complementary and Alternative Medicine Treatments
Dozens of common therapeutic factors have been identified in psychotherapy research, but less attention has been devoted to integrating those factors into coherent theoretical frameworks. Frank and Frank (1991) proposed a comprehensive model with four therapeutic factors common across psychotherapies and other socially-sanctioned healing practices: emotionally charged and confiding relationships with healers, healing settings, persuasive treatment rationales, and specific procedures that engage clients in treatments. They held these factors as powerfully therapeutic because they mobilize hope in otherwise overwhelmed individuals. The current study used multi-group SEM to test Frank and Frank’s model across diverse treatment groups. Rogerian core conditions (empathy, care, genuineness), perceived practitioner credibility, quality of the healing setting, persuasiveness of treatment rationale, and client’s self-assessed hopefulness were measured in five groups of participants. The groups consisted of people receiving treatment for psychological issues from psychotherapists (n = 686) and various complementary and alternative medicine practitioners (n = 155), and those receiving treatment for pain-related issues from chiropractors (n = 518), massage therapists (n = 234), and acupuncturists (n = 100). Results from the cross-sectional model supported Frank and Frank’s hypothesis that their factors independently contribute to the prediction of outcomes across a broad range of healing practices and that their effects are partially mediated by hope. Results from longitudinal analyses based on psychotherapy (n = 138) and chiropractic (n = 134) groups (outcomes measured six to eight months later) showed partial support for Frank and Frank’s model
Mixed diffusive-convective relaxation of a broad beam of energetic particles in cold plasma
We revisit the applications of quasi-linear theory as a paradigmatic model
for weak plasma turbulence and the associated bump-on-tail problem. The work,
presented here, is built around the idea that large-amplitude or strongly
shaped beams do not relax through diffusion only and that there exists an
intermediate time scale where the relaxations are convective (ballistic-like).
We cast this novel idea in the rigorous form of a self-consistent nonlinear
dynamical model, which generalizes the classic equations of the quasi-linear
theory to "broad" beams with internal structure. We also present numerical
simulation results of the relaxation of a broad beam of energetic particles in
cold plasma. These generally demonstrate the mixed diffusive-convective
features of supra-thermal particle transport; and essentially depend on
nonlinear wave-particle interactions and phase-space structures. Taking into
account modes of the stable linear spectrum is crucial for the self-consistent
evolution of the distribution function and the fluctuation intensity spectrum.Comment: 25 pages, 15 figure