441 research outputs found

### Interactions of vortices with rarefaction solitary waves in a Bose-Einstein condensate and their role in the decay of superfluid turbulence

There are several ways to create the vorticity-free solitary waves --
rarefaction pulses -- in condensates: by the process of strongly nonequilibrium
condensate formation in a weakly interacting Bose gas, by creating local
depletion of the condensate density by a laser beam, and by moving a small
object with supercritical velocities. Perturbations created by such waves
colliding with vortices are studied in the context of the Gross-Pitaevskii
model. We find that the effect of the interactions consists of two competing
mechanisms: the creation of vortex line as rarefaction waves acquire
circulation in a vicinity of a vortex core and the loss of the vortex line to
sound due to Kelvin waves that are generated on vortex lines by rarefaction
pulses. When a vortex ring collides with a rarefaction wave, the ring either
stabilises to a smaller ring after emitting sound through Kelvin wave radiation
or the entire energy of the vortex ring is lost to sound if the radius of the
ring is of the order of the healing length. We show that during the time
evolution of a tangle of vortices, the interactions with rarefaction pulses
provide an important dissipation mechanism enhancing the decay of superfluid
turbulence.Comment: Revised paper accepted by Phys. Rev.

### Vortex Splitting in Subcritical Nonlinear Schrodinger Equation

Vortices and axisymmetric vortex rings are considered in the framework of the
subcritical nonlinear Schrodinger equations. The higher order nonlinearity
present in such systems models many-body interactions in superfluid systems and
allows one to study the effects of negative pressure on vortex dynamics. We
find the critical pressure for which the straight-line vortex becomes unstable
to radial expansion of the core. The energy of the straight-line vortices and
energy, impulse and velocity of vortex rings are calculated. The effect of a
varying pressure on the vortex core is studied. It is shown that under the
action of the periodically varying pressure field a vortex ring may split into
many vortex rings and the conditions for which this happens are elucidated.
These processes are also relevant to experiments in Bose-Einstein condensates
where the strength and the sign of two-body interactions can be changed via
Feshbach resonance.Comment: Invited submission to the special issue on Vortex Rings, Journal of
Fluid Dynamics Researc

### Universality in modelling non-equilibrium pattern formation in polariton condensates

The key to understanding the universal behaviour of systems driven away from
equilibrium lies in the common description obtained when particular microscopic
models are reduced to order parameter equations. Universal order parameter
equations written for complex matter fields are widely used to describe systems
as different as Bose-Einstein condensates of ultra cold atomic gases, thermal
convection, nematic liquid crystals, lasers and other nonlinear systems.
Exciton-polariton condensates recently realised in semiconductor microcavities
are pattern forming systems that lie somewhere between equilibrium
Bose-Einstein condensates and lasers. Because of the imperfect confinement of
the photon component, exciton-polaritons have a finite lifetime, and have to be
continuously re-populated. As photon confinement improves, the system more
closely approximates an equilibrium system. In this chapter we review a number
of universal equations which describe various regimes of the dynamics of
exciton-polariton condensates: the Gross-Pitaevskii equation, which models
weakly interacting equilibrium condensates, the complex Ginsburg-Landau
equation---the universal equation that describes the behaviour of systems in
the vicinity of a symmetry--breaking instability, and the complex
Swift-Hohenberg equation that in comparison with the complex Ginsburg-Landau
equation contains additional nonlocal terms responsible for spacial mode
selection. All these equations can be derived asymptotically from a generic
laser model given by Maxwell-Bloch equations. Such an universal framework
allows the unified treatment of various systems and continuously cross from one
system to another. We discuss the relevance of these equations, and their
consequences for pattern formation.Comment: 19 pages; Chapter to appear in Springer&Verlag book on "Quantum
Fluids: hot-topics and new trends" eds. A. Bramati and M. Modugn

### Motion in a Bose condensate: IX. Crow instability of antiparallel vortex pairs

The Gross-Pitaevskii (GP) equation admits a two-dimensional solitary wave
solution representing two mutually self-propelled, anti-parallel straight line
vortices. The complete sequence of such solitary wave solutions has been
computed by Jones and Roberts (J. Phys. A, 15, 2599, 1982). These solutions are
unstable with respect to three-dimensional perturbations (the Crow
instability). The most unstable mode has a wavelength along the direction of
the vortices of the same order as their separation. The growth rate associated
with this mode is evaluated here, and it is found to increase very rapidly with
decreasing separation. It is shown, through numerical integrations of the GP
equation that, as the perturbations grow to finite amplitude, the lines
reconnect to produce a sequence of almost circular vortex rings.Comment: Submitted to J. Phys. A: Math. Gen.; Corrected reference

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