11,008 research outputs found
Josephson tunneling of dark solitons in a double-well potential
We study the dynamics of matter waves in an effectively one-dimensional
Bose-Einstein condensate in a double well potential. We consider in particular
the case when one of the double wells confines excited states. Similarly to the
known ground state oscillations, the states can tunnel between the wells
experiencing the physics known for electrons in a Josephson junction, or be
self-trapped. As the existence of dark solitons in a harmonic trap are
continuations of such non-ground state excitations, one can view the
Josephson-like oscillations as tunnelings of dark solitons. Numerical existence
and stability analysis based on the full equation is performed, where it is
shown that such tunneling can be stable. Through a numerical path following
method, unstable tunneling is also obtained in different parameter regions. A
coupled-mode system is derived and compared to the numerical observations.
Regions of (in)stability of Josephson tunneling are discussed and highlighted.
Finally, we outline an experimental scheme designed to explore such dark
soliton dynamics in the laboratory.Comment: submitte
PT-symmetric sine-Gordon breathers
In this work, we explore a prototypical example of a genuine continuum
breather (i.e., not a standing wave) and the conditions under which it can
persist in a -symmetric medium. As our model of interest, we
will explore the sine-Gordon equation in the presence of a -
symmetric perturbation. Our main finding is that the breather of the
sine-Gordon model will only persist at the interface between gain and loss that
-symmetry imposes but will not be preserved if centered at the
lossy or at the gain side. The latter dynamics is found to be interesting in
its own right giving rise to kink-antikink pairs on the gain side and complete
decay of the breather on the lossy side. Lastly, the stability of the breathers
centered at the interface is studied. As may be anticipated on the basis of
their "delicate" existence properties such breathers are found to be
destabilized through a Hopf bifurcation in the corresponding Floquet analysis
Coupled backward- and forward-propagating solitons in a composite right/left-handed transmission line
We study the coupling between backward- and forward-propagating wave modes,
with the same group velocity, in a composite right/left-handed nonlinear
transmission line. Using an asymptotic multiscale expansion technique, we
derive a system of two coupled nonlinear Schr{\"o}dinger equations governing
the evolution of the envelopes of these modes. We show that this system
supports a variety of backward- and forward propagating vector solitons, of the
bright-bright, bright-dark and dark-bright type. Performing systematic
numerical simulations in the framework of the original lattice that models the
transmission line, we study the propagation properties of the derived vector
soliton solutions. We show that all types of the predicted solitons exist, but
differ on their robustness: only bright-bright solitons propagate undistorted
for long times, while the other types are less robust, featuring shorter
lifetimes. In all cases, our analytical predictions are in a very good
agreement with the results of the simulations, at least up to times of the
order of the solitons' lifetimes
A Unifying Perspective: Solitary Traveling Waves As Discrete Breathers And Energy Criteria For Their Stability
In this work, we provide two complementary perspectives for the (spectral)
stability of solitary traveling waves in Hamiltonian nonlinear dynamical
lattices, of which the Fermi-Pasta-Ulam and the Toda lattice are prototypical
examples. One is as an eigenvalue problem for a stationary solution in a
co-traveling frame, while the other is as a periodic orbit modulo shifts. We
connect the eigenvalues of the former with the Floquet multipliers of the
latter and based on this formulation derive an energy-based spectral stability
criterion. It states that a sufficient (but not necessary) condition for a
change in the wave stability occurs when the functional dependence of the
energy (Hamiltonian) of the model on the wave velocity changes its
monotonicity. Moreover, near the critical velocity where the change of
stability occurs, we provide explicit leading-order computation of the unstable
eigenvalues, based on the second derivative of the Hamiltonian
evaluated at the critical velocity . We corroborate this conclusion with a
series of analytically and numerically tractable examples and discuss its
parallels with a recent energy-based criterion for the stability of discrete
breathers
Two-dimensional discrete solitons in rotating lattices
We introduce a two-dimensional (2D) discrete nonlinear Schr\"{o}dinger (DNLS)
equation with self-attractive cubic nonlinearity in a rotating reference frame.
The model applies to a Bose-Einstein condensate stirred by a rotating strong
optical lattice, or light propagation in a twisted bundle of nonlinear fibers.
Two species of localized states are constructed: off-axis fundamental solitons
(FSs), placed at distance from the rotation pivot, and on-axis (R=0) vortex
solitons (VSs), with vorticities and 2. At a fixed value of rotation
frequency , a stability interval for the FSs is found in terms of the
lattice coupling constant , , with monotonically
decreasing . VSs with S=1 have a stability interval,
\tilde{C}_{\mathrm{cr}%}^{(S=1)}(\Omega),
which exists for below a certain critical value,
. This implies that the VSs with S=1 are
\emph{destabilized} in the weak-coupling limit by the rotation. On the
contrary, VSs with S=2, that are known to be unstable in the standard DNLS
equation, with , are \emph{stabilized} by the rotation in region
%, with growing as a
function of . Quadrupole and octupole on-axis solitons are considered
too, their stability regions being weakly affected by .Comment: To be published in Physical Review
Nucleation of breathers via stochastic resonance in nonlinear lattices
By applying a staggered driving force in a prototypical discrete model with a
quartic nonlinearity, we demonstrate the spontaneous formation and destruction
of discrete breathers with a selected frequency due to thermal fluctuations.
The phenomenon exhibits the striking features of stochastic resonance (SR): a
nonmonotonic behavior as noise is increased and breather generation under
subthreshold conditions. The corresponding peak is associated with a matching
between the external driving frequency and the breather frequency at the
average energy given by ambient temperature.Comment: Added references, figure 5 modified to include new dat
Critical generalized inverse participation ratio distributions
The system size dependence of the fluctuations in generalized inverse
participation ratios (IPR's) at criticality is investigated
numerically. The variances of the IPR logarithms are found to be
scale-invariant at the macroscopic limit. The finite size corrections to the
variances decay algebraically with nontrivial exponents, which depend on the
Hamiltonian symmetry and the dimensionality. The large- dependence of the
asymptotic values of the variances behaves as according to theoretical
estimates. These results ensure the self-averaging of the corresponding
generalized dimensions.Comment: RevTex4, 5 pages, 4 .eps figures, to be published in Phys. Rev.
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