2,023 research outputs found
Discrete Nonlinear Schr{\"o}dinger Breathers in a Phonon Bath
We study the dynamics of the discrete nonlinear Schr{\"o}dinger lattice
initialized such that a very long transitory period of time in which standard
Boltzmann statistics is insufficient is reached. Our study of the nonlinear
system locked in this {\em non-Gibbsian} state focuses on the dynamics of
discrete breathers (also called intrinsic localized modes). It is found that
part of the energy spontaneously condenses into several discrete breathers.
Although these discrete breathers are extremely long lived, their total number
is found to decrease as the evolution progresses. Even though the total number
of discrete breathers decreases we report the surprising observation that the
energy content in the discrete breather population increases. We interpret
these observations in the perspective of discrete breather creation and
annihilation and find that the death of a discrete breather cause effective
energy transfer to a spatially nearby discrete breather. It is found that the
concepts of a multi-frequency discrete breather and of internal modes is
crucial for this process. Finally, we find that the existence of a discrete
breather tends to soften the lattice in its immediate neighborhood, resulting
in high amplitude thermal fluctuation close to an existing discrete breather.
This in turn nucleates discrete breather creation close to a already existing
discrete breather
Matter-wave localization in a random potential
By numerical and variational solution of the Gross-Pitaevskii equation, we
studied the localization of a noninteracting and weakly-interacting
Bose-Einstein condensate (BEC) in a disordered cold atom lattice and a speckle
potential. In the case of a single BEC fragment, the variational analysis
produced good results. For a weakly disordered potential, the localized BECs
are found to have an exponential tail as in weak Anderson localization. We also
investigated the expansion of a noninteracting BEC in these potential. We find
that the BEC will be locked in an appropriate localized state after an initial
expansion and will execute breathing oscillation around a mean shape when a BEC
at equilibrium in a harmonic trap is suddenly released into a disorder
potential
Metal-insulator transition in an aperiodic ladder network: an exact result
We show, in a completely analytical way, that a tight binding ladder network
composed of atomic sites with on-site potentials distributed according to the
quasiperiodic Aubry model can exhibit a metal-insulator transition at multiple
values of the Fermi energy. For specific values of the first and second
neighbor electron hopping, the result is obtained exactly. With a more general
model, we calculate the two-terminal conductance numerically. The numerical
results corroborate the analytical findings and yield a richer variety of
spectrum showing multiple mobility edges.Comment: 4 pages, 3 figure
Absence of Wavepacket Diffusion in Disordered Nonlinear Systems
We study the spreading of an initially localized wavepacket in two nonlinear
chains (discrete nonlinear Schroedinger and quartic Klein-Gordon) with
disorder. Previous studies suggest that there are many initial conditions such
that the second moment of the norm and energy density distributions diverge as
a function of time. We find that the participation number of a wavepacket does
not diverge simultaneously. We prove this result analytically for
norm-conserving models and strong enough nonlinearity. After long times the
dynamical state consists of a distribution of nondecaying yet interacting
normal modes. The Fourier spectrum shows quasiperiodic dynamics. Assuming this
result holds for any initially localized wavepacket, a limit profile for the
norm/energy distribution with infinite second moment should exist in all cases
which rules out the possibility of slow energy diffusion (subdiffusion). This
limit profile could be a quasiperiodic solution (KAM torus)
The Exact Ground State of the Frenkel-Kontorova Model with Repeated Parabolic Potential: I. Basic Results
The problem of finding the exact energies and configurations for the
Frenkel-Kontorova model consisting of particles in one dimension connected to
their nearest-neighbors by springs and placed in a periodic potential
consisting of segments from parabolas of identical (positive) curvature but
arbitrary height and spacing, is reduced to that of minimizing a certain convex
function defined on a finite simplex.Comment: 12 RevTeX pages, using AMS-Fonts (amssym.tex,amssym.def), 6
Postscript figures, accepted by Phys. Rev.
Surface spin-flop phases and bulk discommensurations in antiferromagnets
Phase diagrams as a function of anisotropy D and magnetic field H are
obtained for discommensurations and surface states for a model antiferromagnet
in which is parallel to the easy axis. The surface spin-flop phase exists
for all . We show that there is a region where the penetration length of the
surface spin-flop phase diverges. Introducing a discommensuration of even
length then becomes preferable to reconstructing the surface. The results are
used to clarify and correct previous studies in which discommensurations have
been confused with genuine surface spin-flop states.Comment: 4 pages, RevTeX, 2 Postscript figure
Localization of a Bose-Einstein condensate vortex in a bichromatic optical lattice
By numerical simulation of the time-dependent Gross-Pitaevskii equation we
show that a weakly interacting or noninteracting Bose-Einstein condensate (BEC)
vortex can be localized in a three-dimensional bichromatic quasi-periodic
optical-lattice (OL) potential generated by the superposition of two
standing-wave polarized laser beams with incommensurate wavelengths. This is a
generalization of the localization of a BEC in a one-dimensional bichromatic OL
as studied in a recent experiment [Roati et al., Nature 453, 895 (2008)]. We
demonstrate the stability of the localized state by considering its time
evolution in the form of a stable breathing oscillation in a slightly altered
potential for a large period of time. {Finally, we consider the localization of
a BEC in a random 1D potential in the form of several identical repulsive
spikes arbitrarily distributed in space
Localization of a Bose-Einstein condensate in a bichromatic optical lattice
By direct numerical simulation of the time-dependent Gross-Pitaevskii
equation we study different aspects of the localization of a non-interacting
ideal Bose-Einstein condensate (BEC) in a one-dimensional bichromatic
quasi-periodic optical-lattice potential. Such a quasi-periodic potential, used
in a recent experiment on the localization of a BEC [Roati et al., Nature 453,
895 (2008)], can be formed by the superposition of two standing-wave polarized
laser beams with different wavelengths. We investigate the effect of the
variation of optical amplitudes and wavelengths on the localization of a
non-interacting BEC. We also simulate the non-linear dynamics when a
harmonically trapped BEC is suddenly released into a quasi-periodic potential,
{as done experimentally in a laser speckle potential [Billy et al., Nature 453,
891 (2008)]$ We finally study the destruction of the localization in an
interacting BEC due to the repulsion generated by a positive scattering length
between the bosonic atoms.Comment: 8 page
Localization of a dipolar Bose-Einstein condensate in a bichromatic optical lattice
By numerical simulation and variational analysis of the Gross-Pitaevskii
equation we study the localization, with an exponential tail, of a dipolar
Bose-Einstein condensate (DBEC) of Cr atoms in a three-dimensional
bichromatic optical-lattice (OL) generated by two monochromatic OL of
incommensurate wavelengths along three orthogonal directions. For a fixed
dipole-dipole interaction, a localized state of a small number of atoms () could be obtained when the short-range interaction is not too attractive
or not too repulsive. A phase diagram showing the region of stability of a DBEC
with short-range interaction and dipole-dipole interaction is given
- …