10,425 research outputs found
Anderson transition in systems with chiral symmetry
Anderson localization is a universal quantum feature caused by destructive
interference. On the other hand chiral symmetry is a key ingredient in
different problems of theoretical physics: from nonperturbative QCD to highly
doped semiconductors. We investigate the interplay of these two phenomena in
the context of a three-dimensional disordered system. We show that chiral
symmetry induces an Anderson transition (AT) in the region close to the band
center. Typical properties at the AT such as multifractality and critical
statistics are quantitatively affected by this additional symmetry. The origin
of the AT has been traced back to the power-law decay of the eigenstates; this
feature may also be relevant in systems without chiral symmetry.Comment: RevTex4, 4 two-column pages, 3 .eps figures, updated references,
final version as published in Phys. Rev.
Non-ergodic phases in strongly disordered random regular graphs
We combine numerical diagonalization with a semi-analytical calculations to
prove the existence of the intermediate non-ergodic but delocalized phase in
the Anderson model on disordered hierarchical lattices. We suggest a new
generalized population dynamics that is able to detect the violation of
ergodicity of the delocalized states within the Abou-Chakra, Anderson and
Thouless recursive scheme. This result is supplemented by statistics of random
wave functions extracted from exact diagonalization of the Anderson model on
ensemble of disordered Random Regular Graphs (RRG) of N sites with the
connectivity K=2. By extrapolation of the results of both approaches to
N->infinity we obtain the fractal dimensions D_{1}(W) and D_{2}(W) as well as
the population dynamic exponent D(W) with the accuracy sufficient to claim that
they are non-trivial in the broad interval of disorder strength W_{E}<W<W_{c}.
The thorough analysis of the exact diagonalization results for RRG with
N>10^{5} reveals a singularity in D_{1,2}(W)-dependencies which provides a
clear evidence for the first order transition between the two delocalized
phases on RRG at W_{E}\approx 10.0. We discuss the implications of these
results for quantum and classical non-integrable and many-body systems.Comment: 4 pages paper with 5 figures + Supplementary Material with 5 figure
Breathers in inhomogeneous nonlinear lattices: an analysis via centre manifold reduction
We consider an infinite chain of particles linearly coupled to their nearest
neighbours and subject to an anharmonic local potential. The chain is assumed
weakly inhomogeneous. We look for small amplitude discrete breathers. The
problem is reformulated as a nonautonomous recurrence in a space of
time-periodic functions, where the dynamics is considered along the discrete
spatial coordinate. We show that small amplitude oscillations are determined by
finite-dimensional nonautonomous mappings, whose dimension depends on the
solutions frequency. We consider the case of two-dimensional reduced mappings,
which occurs for frequencies close to the edges of the phonon band. For an
homogeneous chain, the reduced map is autonomous and reversible, and
bifurcations of reversible homoclinics or heteroclinic solutions are found for
appropriate parameter values. These orbits correspond respectively to discrete
breathers, or dark breathers superposed on a spatially extended standing wave.
Breather existence is shown in some cases for any value of the coupling
constant, which generalizes an existence result obtained by MacKay and Aubry at
small coupling. For an inhomogeneous chain the study of the nonautonomous
reduced map is in general far more involved. For the principal part of the
reduced recurrence, using the assumption of weak inhomogeneity, we show that
homoclinics to 0 exist when the image of the unstable manifold under a linear
transformation intersects the stable manifold. This provides a geometrical
understanding of tangent bifurcations of discrete breathers. The case of a mass
impurity is studied in detail, and our geometrical analysis is successfully
compared with direct numerical simulations
The main runs and datasets of the Fine Resolution Antarctic Model Project (FRAM). Part I: the coarse resolution runs
Bright and dark breathers in Fermi-Pasta-Ulam lattices
In this paper we study the existence and linear stability of bright and dark
breathers in one-dimensional FPU lattices. On the one hand, we test the range
of validity of a recent breathers existence proof [G. James, {\em C. R. Acad.
Sci. Paris}, 332, Ser. 1, pp. 581 (2001)] using numerical computations.
Approximate analytical expressions for small amplitude bright and dark
breathers are found to fit very well exact numerical solutions even far from
the top of the phonon band. On the other hand, we study numerically large
amplitude breathers non predicted in the above cited reference. In particular,
for a class of asymmetric FPU potentials we find an energy threshold for the
existence of exact discrete breathers, which is a relatively unexplored
phenomenon in one-dimensional lattices. Bright and dark breathers superposed on
a uniformly stressed static configuration are also investigated.Comment: 11 pages, 16 figure
Breathers in FPU systems, near and far from the phonon band
There exists a recent mathematical proof on the existence of small amplitude
breathers in FPU systems near the phonon band, which includes a prediction of
their amplitude and width. In this work we obtain numerically these breathers,
and calculate the range of validity of the predictions, which extends
relatively far from the phonon band. There exist also large amplitude breathers
with the same frequency, with the consequence that there is an energy gap for
breather creation in these systems.Comment: 3 pages, 2 figures, proceeding of the conference on Localization and
to and Energy Transfer in Nonlinear Systems, June 17-21, 2002, San Lorenzo de
El Escorial, Madrid, Spain. To be published by World Scientifi
Solitary waves in a two-dimensional nonlinear Dirac equation: from discrete to continuum
In the present work, we explore a nonlinear Dirac equation motivated as the
continuum limit of a binary waveguide array model. We approach the problem both
from a near-continuum perspective as well as from a highly discrete one.
Starting from the former, we see that the continuum Dirac solitons can be
continued for all values of the discretization (coupling) parameter, down to
the uncoupled (so-called anti-continuum) limit where they result in a 9-site
configuration. We also consider configurations with 1- or 2-sites at the
anti-continuum limit and continue them to large couplings, finding that they
also persist. For all the obtained solutions, we examine not only the
existence, but also the spectral stability through a linearization analysis and
finally consider prototypical examples of the dynamics for a selected number of
cases for which the solutions are found to be unstable
Stabilization of the Peregrine soliton and Kuznetsov-Ma breathers by means of nonlinearity and dispersion management
We demonstrate a possibility to make rogue waves (RWs) in the form of the
Peregrine soliton (PS) and Kuznetsov-Ma breathers (KMBs) effectively stable
objects, with the help of properly defined dispersion or nonlinearity
management applied to the continuous-wave (CW) background supporting the RWs.
In particular, it is found that either management scheme, if applied along the
longitudinal coordinate, making the underlying nonlinear Schr\"odinger equation
(NLSE) selfdefocusing in the course of disappearance of the PS, indeed
stabilizes the global solution with respect to the modulational instability of
the background. In the process, additional excitations are generated, namely,
dispersive shock waves and, in some cases, also a pair of slowly separating
dark solitons. Further, the nonlinearity-management format, which makes the
NLSE defocusing outside of a finite domain in the transverse direction, enables
the stabilization of the KMBs, in the form of confined oscillating states. On
the other hand, a nonlinearity-management format applied periodically along the
propagation direction, creates expanding patterns featuring multiplication of
KMBs through their cascading fission.Comment: Physics Letters A, on pres
Level number variance and spectral compressibility in a critical two-dimensional random matrix model
We study level number variance in a two-dimensional random matrix model
characterized by a power-law decay of the matrix elements. The amplitude of the
decay is controlled by the parameter b. We find analytically that at small
values of b the level number variance behaves linearly, with the
compressibility chi between 0 and 1, which is typical for critical systems. For
large values of b, we derive that chi=0, as one would normally expect in the
metallic phase. Using numerical simulations we determine the critical value of
b at which the transition between these two phases occurs.Comment: 6 page
Collective Coordinates Theory for Discrete Soliton Ratchets in the sine-Gordon Model
A collective coordinate theory is develop for soliton ratchets in the damped
discrete sine-Gordon model driven by a biharmonic force. An ansatz with two
collective coordinates, namely the center and the width of the soliton, is
assumed as an approximated solution of the discrete non-linear equation. The
evolution of these two collective coordinates, obtained by means of the
Generalized Travelling Wave Method, explains the mechanism underlying the
soliton ratchet and captures qualitatively all the main features of this
phenomenon. The theory accounts for the existence of a non-zero depinning
threshold, the non-sinusoidal behaviour of the average velocity as a function
of the difference phase between the harmonics of the driver, the non-monotonic
dependence of the average velocity on the damping and the existence of
non-transporting regimes beyond the depinning threshold. In particular it
provides a good description of the intriguing and complex pattern of subspaces
corresponding to different dynamical regimes in parameter space
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