507 research outputs found
Dirac fermions in a power-law-correlated random vector potential
We study localization properties of two-dimensional Dirac fermions subject to
a power-law-correlated random vector potential describing, e.g., the effect of
"ripples" in graphene. By using a variety of techniques (low-order perturbation
theory, self-consistent Born approximation, replicas, and supersymmetry) we
make a case for a possible complete localization of all the electronic states
and compute the density of states.Comment: Latex, 4+ page
Informatics Higher Education in Europe: A Data Portal and Case Study
A discussion on the need for coordinated, governed, data-driven computing education initiatives of the future
Observation of dipole-mode vector solitons
We report on the first experimental observation of a novel type of optical
vector soliton, a {\em dipole-mode soliton}, recently predicted theoretically.
We show that these vector solitons can be generated in a photorefractive medium
employing two different processes: a phase imprinting, and a symmetry-breaking
instability of a vortex-mode vector soliton. The experimental results display
remarkable agreement with the theory, and confirm the robust nature of these
radially asymmetric two-component solitary waves.Comment: 4 pages, 8 figures; pictures in the PRL version are better qualit
Svortices and the fundamental modes of the "snake instability": Possibility of observation in the gaseous Bose-Einstein Condensate
The connection between quantized vortices and dark solitons in a long and
thin, waveguide-like trap geometry is explored in the framework of the
non-linear Schr\"odinger equation. Variation of the transverse confinement
leads from the quasi-1D regime where solitons are stable to 2D (or 3D)
confinement where soliton stripes are subject to a transverse modulational
instability known as the ``snake instability''. We present numerical evidence
of a regime of intermediate confinement where solitons decay into single,
deformed vortices with solitonic properties, also called svortices, rather than
vortex pairs as associated with the ``snake'' metaphor. Further relaxing the
transverse confinement leads to production of 2 and then 3 vortices, which
correlates perfectly with a Bogoliubov-de Gennes stability analysis. The decay
of a stationary dark soliton (or, planar node) into a single svortex is
predicted to be experimentally observable in a 3D harmonically confined dilute
gas Bose-Einstein condensate.Comment: 4 pages, 4 figure
Watching dark solitons decay into vortex rings in a Bose-Einstein condensate
We have created spatial dark solitons in two-component Bose-Einstein
condensates in which the soliton exists in one of the condensate components and
the soliton nodal plane is filled with the second component. The filled
solitons are stable for hundreds of milliseconds. The filling can be
selectively removed, making the soliton more susceptible to dynamical
instabilities. For a condensate in a spherically symmetric potential, these
instabilities cause the dark soliton to decay into stable vortex rings. We have
imaged the resulting vortex rings.Comment: 4 pages, 4 figure
Instabilities of Higher-Order Parametric Solitons. Filamentation versus Coalescence
We investigate stability and dynamics of higher-order solitary waves in
quadratic media, which have a central peak and one or more surrounding rings.
We show existence of two qualitatively different behaviours. For positive phase
mismatch the rings break up into filaments which move radially to initial ring.
For sufficient negative mismatches rings are found to coalesce with central
peak, forming a single oscillating filament.Comment: 5 pages, 7 figure
Induced Coherence and Stable Soliton Spiraling
We develop a theory of soliton spiraling in a bulk nonlinear medium and
reveal a new physical mechanism: periodic power exchange via induced coherence,
which can lead to stable spiraling and the formation of dynamical two-soliton
states. Our theory not only explains earlier observations, but provides a
number of predictions which are also verified experimentally. Finally, we show
theoretically and experimentally that soliton spiraling can be controled by the
degree of mutual initial coherence.Comment: 4 pages, 5 figure
Split Instability of a Vortex in an Attractive Bose-Einstein Condensate
An attractive Bose-Einstein condensate with a vortex splits into two pieces
via the quadrupole dynamical instability, which arises at a weaker strength of
interaction than the monopole and the dipole instabilities. The split pieces
subsequently unite to restore the original vortex or collapse.Comment: 4 pages, 4 figures, added figures and references, revised tex
Nonlinear Waves in Bose-Einstein Condensates: Physical Relevance and Mathematical Techniques
The aim of the present review is to introduce the reader to some of the
physical notions and of the mathematical methods that are relevant to the study
of nonlinear waves in Bose-Einstein Condensates (BECs). Upon introducing the
general framework, we discuss the prototypical models that are relevant to this
setting for different dimensions and different potentials confining the atoms.
We analyze some of the model properties and explore their typical wave
solutions (plane wave solutions, bright, dark, gap solitons, as well as
vortices). We then offer a collection of mathematical methods that can be used
to understand the existence, stability and dynamics of nonlinear waves in such
BECs, either directly or starting from different types of limits (e.g., the
linear or the nonlinear limit, or the discrete limit of the corresponding
equation). Finally, we consider some special topics involving more recent
developments, and experimental setups in which there is still considerable need
for developing mathematical as well as computational tools.Comment: 69 pages, 10 figures, to appear in Nonlinearity, 2008. V2: new
references added, fixed typo
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