210 research outputs found
Dark solitons and vortices in PT-symmetric nonlinear media: from spontaneous symmetry breaking to nonlinear PT phase transitions
We consider nonlinear analogues of Parity-Time (PT) symmetric linear systems
exhibiting defocusing nonlinearities. We study the ground state and excited
states (dark solitons and vortices) of the system and report the following
remarkable features. For relatively weak values of the parameter
controlling the strength of the PT-symmetric potential, excited states undergo
(analytically tractable) spontaneous symmetry breaking; as is
further increased, the ground state and first excited state, as well as
branches of higher multi-soliton (multi-vortex) states, collide in pairs and
disappear in blue-sky bifurcations, in a way which is strongly reminiscent of
the linear PT-phase transition ---thus termed the nonlinear PT-phase
transition. Past this critical point, initialization of, e.g., the former
ground state leads to spontaneously emerging solitons and vortices.Comment: 8 pages, 8 figure
Discrete Breathers in a Nonlinear Polarizability Model of Ferroelectrics
We present a family of discrete breathers, which exists in a nonlinear
polarizability model of ferroelectric materials. The core-shell model is set up
in its non-dimensionalized Hamiltonian form and its linear spectrum is
examined. Subsequently, seeking localized solutions in the gap of the linear
spectrum, we establish that numerically exact and potentially stable discrete
breathers exist for a wide range of frequencies therein.
In addition, we present nonlinear normal mode, extended spatial profile
solutions from which the breathers bifurcate, as well as other associated
phenomena such as the formation of phantom breathers within the model.
The full bifurcation picture of the emergence and disappearance of the
breathers is complemented by direct numerical simulations of their dynamical
instability, when the latter arises.Comment: 9 pages, 7 figures, 1 tabl
Dynamical Superfluid-Insulator Transition in a Chain of Weakly Coupled Bose-Einstein Condensates
We predict a dynammical classical superfluid-insulator transition (CSIT) in a
Bose-Einstein condensate (BEC) trapped in an optical and a magnetic potential.
In the tight-binding limit, this system realizes an array of weakly-coupled
condensates driven by an external harmonic field. For small displacements of
the parabolic trap about the equilibrium position, the BEC center of mass
oscillates with the relative phases of neighbouring condensates locked at the
same (oscillating) value. For large displacements, the BEC remains localized on
the side of the harmonic trap. This is caused by a randomization of the
relative phases, while the coherence of each individual condensate in the array
is preserved. The CSIT is attributed to a discrete modulational instability,
occurring when the BEC center of mass velocity is larger than a critical value,
proportional to the tunneling rate between adjacent sites.Comment: 5 pages, 4 figures, to appear in Phys. Rev. Let
Coarse-grained computations of demixing in dense gas-fluidized beds
We use an "equation-free", coarse-grained computational approach to
accelerate molecular dynamics-based computations of demixing (segregation) of
dissimilar particles subject to an upward gas flow (gas-fluidized beds). We
explore the coarse-grained dynamics of these phenomena in gently fluidized beds
of solid mixtures of different densities, typically a slow process for which
reasonable continuum models are currently unavailable
Vortices in Bose-Einstein Condensates: Some Recent Developments
In this brief review we summarize a number of recent developments in the
study of vortices in Bose-Einstein condensates, a topic of considerable
theoretical and experimental interest in the past few years. We examine the
generation of vortices by means of phase imprinting, as well as via dynamical
instabilities. Their stability is subsequently examined in the presence of
purely magnetic trapping, and in the combined presence of magnetic and optical
trapping. We then study pairs of vortices and their interactions, illustrating
a reduced description in terms of ordinary differential equations for the
vortex centers. In the realm of two vortices we also consider the existence of
stable dipole clusters for two-component condensates. Last but not least, we
discuss mesoscopic patterns formed by vortices, the so-called vortex lattices
and analyze some of their intriguing dynamical features. A number of
interesting future directions are highlighted.Comment: 24 pages, 8 figs, ws-mplb.cls, to appear in Modern Physics Letters B
(2005
Nonlinear Excitations, Stability Inversions and Dissipative Dynamics in Quasi-one-dimensional Polariton Condensates
We consider the existence, stability and dynamics of the ground state and
nonlinear excitations, in the form of dark solitons, for a
quasi-one-dimensional polariton condensate in the presence of pumping and
nonlinear damping. We find a series of remarkable features that can be directly
contrasted to the case of the typically energy-conserving ultracold alkali-atom
Bose-Einstein condensates. For some sizeable parameter ranges, the nodeless
("ground") state becomes {\it unstable} towards the formation of {\em stable}
nonlinear single or {\em multi} dark-soliton excitations. It is also observed
that for suitable parametric choices, the instability of single dark solitons
can nucleate multi-dark-soliton states. Also, for other parametric regions,
{\em stable asymmetric} sawtooth-like solutions exist. Finally, we consider the
dragging of a defect through the condensate and the interference of two
initially separated condensates, both of which are capable of nucleating dark
multi-soliton dynamical states.Comment: 9 pages, 10 figure
Solitary Waves Under the Competition of Linear and Nonlinear Periodic Potentials
In this paper, we study the competition of linear and nonlinear lattices and
its effects on the stability and dynamics of bright solitary waves. We consider
both lattices in a perturbative framework, whereby the technique of Hamiltonian
perturbation theory can be used to obtain information about the existence of
solutions, and the same approach, as well as eigenvalue count considerations,
can be used to obtained detailed conditions about their linear stability. We
find that the analytical results are in very good agreement with our numerical
findings and can also be used to predict features of the dynamical evolution of
such solutions.Comment: 13 pages, 4 figure
Pattern Forming Dynamical Instabilities of Bose-Einstein Condensates: A Short Review
In this short topical review, we revisit a number of works on the
pattern-forming dynamical instabilities of Bose-Einstein condensates in one-
and two-dimensional settings. In particular, we illustrate the trapping
conditions that allow the reduction of the three-dimensional, mean field
description of the condensates (through the Gross-Pitaevskii equation) to such
lower dimensional settings, as well as to lattice settings. We then go on to
study the modulational instability in one dimension and the snaking/transverse
instability in two dimensions as typical examples of long-wavelength
perturbations that can destabilize the condensates and lead to the formation of
patterns of coherent structures in them. Trains of solitons in one-dimension
and vortex arrays in two-dimensions are prototypical examples of the resulting
nonlinear waveforms, upon which we briefly touch at the end of this review.Comment: 28 pages, 9 figures, publishe
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