4 research outputs found
Spreading, Nonergodicity, and Selftrapping: a puzzle of interacting disordered lattice waves
Localization of waves by disorder is a fundamental physical problem
encompassing a diverse spectrum of theoretical, experimental and numerical
studies in the context of metal-insulator transitions, the quantum Hall effect,
light propagation in photonic crystals, and dynamics of ultra-cold atoms in
optical arrays, to name just a few examples. Large intensity light can induce
nonlinear response, ultracold atomic gases can be tuned into an interacting
regime, which leads again to nonlinear wave equations on a mean field level.
The interplay between disorder and nonlinearity, their localizing and
delocalizing effects is currently an intriguing and challenging issue in the
field of lattice waves. In particular it leads to the prediction and
observation of two different regimes of destruction of Anderson localization -
asymptotic weak chaos, and intermediate strong chaos, separated by a crossover
condition on densities. On the other side approximate full quantum interacting
many body treatments were recently used to predict and obtain a novel many body
localization transition, and two distinct phases - a localization phase, and a
delocalization phase, both again separated by some typical density scale. We
will discuss selftrapping, nonergodicity and nonGibbsean phases which are
typical for such discrete models with particle number conservation and their
relation to the above crossover and transition physics. We will also discuss
potential connections to quantum many body theories.Comment: 13 pages in Springer International Publishing Switzerland 2016 1 M.
Tlidi and M. G. Clerc (eds.), Nonlinear Dynamics: Materials, Theory and
Experiment, Springer Proceedings in Physics 173. arXiv admin note: text
overlap with arXiv:1405.112
Thermal conductivity of nonlinear waves in disordered chains
We present computational data on the thermal conductivity of nonlinear waves
in disordered chains. Disorder induces Anderson localization for linear waves
and results in a vanishing conductivity. Cubic nonlinearity restores normal
conductivity, but with a strongly temperature-dependent conductivity
. We find indications for an asymptotic low-temperature and intermediate temperature laws. These findings are in
accord with theoretical studies of wave packet spreading, where a regime of
strong chaos is found to be intermediate, followed by an asymptotic regime of
weak chaos (EPL 91 (2010) 30001).Comment: 8 pages, 3 figure