24 research outputs found
Re-localization due to finite response times in a nonlinear Anderson chain
We study a disordered nonlinear Schr\"odinger equation with an additional
relaxation process having a finite response time . Without the relaxation
term, , this model has been widely studied in the past and numerical
simulations showed subdiffusive spreading of initially localized excitations.
However, recently Caetano et al.\ (EPJ. B \textbf{80}, 2011) found that by
introducing a response time , spreading is suppressed and any
initially localized excitation will remain localized. Here, we explain the lack
of subdiffusive spreading for by numerically analyzing the energy
evolution. We find that in the presence of a relaxation process the energy
drifts towards the band edge, which enforces the population of fewer and fewer
localized modes and hence leads to re-localization. The explanation presented
here is based on previous findings by the authors et al.\ (PRE \textbf{80},
2009) on the energy dependence of thermalized states.Comment: 3 pages, 4 figure
Impurity in a Bose-Einstein condensate in a double well
We compare and contrast the mean-field and many-body properties of a
Bose-Einstein condensate trapped in a double well potential with a single
impurity atom. The mean-field solutions display a rich structure of
bifurcations as parameters such as the boson-impurity interaction strength and
the tilt between the two wells are varied. In particular, we study a pitchfork
bifurcation in the lowest mean-field stationary solution which occurs when the
boson-impurity interaction exceeds a critical magnitude. This bifurcation,
which is present for both repulsive and attractive boson-impurity interactions,
corresponds to the spontaneous formation of an imbalance in the number of
particles between the two wells. If the boson-impurity interaction is large,
the bifurcation is associated with the onset of a Schroedinger cat state in the
many-body ground state. We calculate the coherence and number fluctuations
between the two wells, and also the entanglement entropy between the bosons and
the impurity. We find that the coherence can be greatly enhanced at the
bifurcation.Comment: 19 pages, 17 figures. The second version contains minor corrections
and some better figures (thicker lines
Drastic fall-off of the thermal conductivity for disordered lattices in the limit of weak anharmonic interactions
We study the thermal conductivity, at fixed positive temperature, of a
disordered lattice of harmonic oscillators, weakly coupled to each other
through anharmonic potentials. The interaction is controlled by a small
parameter . We rigorously show, in two slightly different setups,
that the conductivity has a non-perturbative origin. This means that it decays
to zero faster than any polynomial in as . It
is then argued that this result extends to a disordered chain studied by Dhar
and Lebowitz, and to a classical spins chain recently investigated by
Oganesyan, Pal and Huse.Comment: 21 page
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
Nonlinear Lattice Waves in Random Potentials
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 transition, quantum Hall effect,
light propagation in photonic crystals, and dynamics of ultra-cold atoms in
optical arrays. 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. We will discuss recent advances
in the dynamics of nonlinear lattice waves in random potentials. In the absence
of nonlinear terms in the wave equations, Anderson localization is leading to a
halt of wave packet spreading.
Nonlinearity couples localized eigenstates and, potentially, enables
spreading and destruction of Anderson localization due to nonintegrability,
chaos and decoherence. The spreading process is characterized by universal
subdiffusive laws due to nonlinear diffusion. We review extensive computational
studies for one- and two-dimensional systems with tunable nonlinearity power.
We also briefly discuss extensions to other cases where the linear wave
equation features localization: Aubry-Andre localization with quasiperiodic
potentials, Wannier-Stark localization with dc fields, and dynamical
localization in momentum space with kicked rotors.Comment: 45 pages, 19 figure
The Nonlinear Schroedinger Equation with a random potential: Results and Puzzles
The Nonlinear Schroedinger Equation (NLSE) with a random potential is
motivated by experiments in optics and in atom optics and is a paradigm for the
competition between the randomness and nonlinearity. The analysis of the NLSE
with a random (Anderson like) potential has been done at various levels of
control: numerical, analytical and rigorous. Yet, this model equation presents
us with a highly inconclusive and often contradictory picture. We will describe
the main recent results obtained in this field and propose a list of specific
problems to focus on, that we hope will enable to resolve these outstanding
questions.Comment: 21 pages, 4 figure