31 research outputs found
A concentration phenomenon for semilinear elliptic equations
For a domain \Omega\subset\dR^N we consider the equation -\Delta u +
V(x)u = Q_n(x)\abs{u}^{p-2}u with zero Dirichlet boundary conditions and
. Here and are bounded functions that are positive
in a region contained in and negative outside, and such that the sets
shrink to a point as . We show that if
is a nontrivial solution corresponding to , then the sequence
concentrates at with respect to the and certain
-norms. We also show that if the sets shrink to two points and
are ground state solutions, then they concentrate at one of these points
Surface Gap Soliton Ground States for the Nonlinear Schr\"{o}dinger Equation
We consider the nonlinear Schr\"{o}dinger equation , with and and with periodic in each coordinate direction. This problem
describes the interface of two periodic media, e.g. photonic crystals. We study
the existence of ground state solutions (surface gap soliton ground
states) for . Using a concentration compactness
argument, we provide an abstract criterion for the existence based on ground
state energies of each periodic problem (with and ) as well as a more practical
criterion based on ground states themselves. Examples of interfaces satisfying
these criteria are provided. In 1D it is shown that, surprisingly, the criteria
can be reduced to conditions on the linear Bloch waves of the operators
and .Comment: definition of ground and bound states added, assumption (H2) weakened
(sign changing nonlinearity is now allowed); 33 pages, 4 figure
Backward Cherenkov radiation emitted by polariton solitons in a microcavity wire
Exciton-polaritons in semiconductor microcavities form a highly nonlinear platform to study a variety of effects interfacing optical, condensed matter, quantum and statistical physics. We show that the complex polariton patterns generated by picosecond pulses in microcavity wire waveguides can be understood as the Cherenkov radiation emitted by bright polariton solitons, which is enabled by the unique microcavity polariton dispersion, which has momentum intervals with positive and negative group velocities. Unlike in optical fibres and semiconductor waveguides, we observe that the microcavity wire Cherenkov radiation is predominantly emitted with negative group velocity and therefore propagates backwards relative to the propagation direction of the emitting soliton. We have developed a theory of the microcavity wire polariton solitons and of their Cherenkov radiation and conducted a series of experiments, where we have measured polariton-soliton pulse compression, pulse breaking and emission of the backward Cherenkov radiation
Instabilities in the two-dimensional cubic nonlinear Schrodinger equation
The two-dimensional cubic nonlinear Schrodinger equation (NLS) can be used as
a model of phenomena in physical systems ranging from waves on deep water to
pulses in optical fibers. In this paper, we establish that every
one-dimensional traveling wave solution of NLS with trivial phase is unstable
with respect to some infinitesimal perturbation with two-dimensional structure.
If the coefficients of the linear dispersion terms have the same sign then the
only unstable perturbations have transverse wavelength longer than a
well-defined cut-off. If the coefficients of the linear dispersion terms have
opposite signs, then there is no such cut-off and as the wavelength decreases,
the maximum growth rate approaches a well-defined limit.Comment: 4 pages, 4 figure
The Potential Role of Migratory Birds in the Spread of Tick-borne Infections in Siberia and the Russian Far East
AbstractFrom 2006 to 2011, in the Tomsk region (south of Western Siberia), eight species of pathogens were detected in birds and the ticks feeding on them: Tick-borne encephalitis virus (TBEV), West Nile virus (WNV), Borrelia spp., Rickettsia spp., Bartonella spp., Anaplasma spp., Ehrlichia spp., and Babesia spp. The identification of a number of strains of viruses and bacterial genovariants related geographically with the Russian Far East, Eastern Siberia, China and Japan and confirms the possibility of the role of birds in the spread of pathogens in the direction of Western Siberia and back. Most of the species that breed and migrate in Western Siberia are of Eastern origin and mostly fly for wintering to South-East Asia. Among these species in our samples, Phylloscopus proregulus was a carrier of both TBEV and Bartonella spp.; Luscinia calliope were infected with both TBEV and Borrelia, while Tarsiger cyanurus were infected with WNV
Scattering of dipole-mode vector solitons: Theory and experiment
We study, both theoretically and experimentally, the scattering properties of
optical dipole-mode vector solitons - radially asymmetric composite
self-trapped optical beams. First, we analyze the soliton collisions in an
isotropic two-component model with a saturable nonlinearity and demonstrate
that in many cases the scattering dynamics of the dipole-mode solitons allows
us to classify them as ``molecules of light'' - extremely robust spatially
localized objects which survive a wide range of interactions and display many
properties of composite states with a rotational degree of freedom. Next, we
study the composite solitons in an anisotropic nonlinear model that describes
photorefractive nonlinearities, and also present a number of experimental
verifications of our analysis.Comment: 8 pages + 4 pages of figure
One-dimension cubic-quintic Gross-Pitaevskii equation in Bose-Einstein condensates in a trap potential
By means of new general variational method we report a direct solution for
the quintic self-focusing nonlinearity and cubic-quintic 1D Gross Pitaeskii
equation (GPE) in a harmonic confined potential. We explore the influence of
the 3D transversal motion generating a quintic nonlinear term on the ideal 1D
pure cigar-like shape model for the attractive and repulsive atom-atom
interaction in Bose Einstein condensates (BEC). Also, we offer a closed
analytical expression for the evaluation of the error produced when solely the
cubic nonlinear GPE is considered for the description of 1D BEC.Comment: 6 pages, 3 figure
Superfluid rotation sensor with helical laser trap
The macroscopic quantum states of the dilute bosonic ensemble in helical
laser trap at the temperatures about are considered in the
framework of the Gross-Pitaevskii equation. The helical interference pattern is
composed of the two counter propagating Laguerre-Gaussian optical vortices with
opposite orbital angular momenta and this pattern is driven in
rotation via angular Doppler effect. Macroscopic observables including linear
momentum and angular momentum of the atomic cloud are evaluated explicitly. It
is shown that rotation of reference frame is transformed into translational
motion of the twisted matter wave. The speed of translation equals the group
velocity of twisted wavetrain and alternates with a sign
of the frame angular velocity and helical pattern handedness .
We address detection of this effect using currently accessible laboratory
equipment with emphasis on the difference between quantum and classical fluids.Comment: 8 pages, 3 figures, accepted to publication Journ.Low Temp.Phy
From Coherent Modes to Turbulence and Granulation of Trapped Gases
The process of exciting the gas of trapped bosons from an equilibrium initial
state to strongly nonequilibrium states is described as a procedure of symmetry
restoration caused by external perturbations. Initially, the trapped gas is
cooled down to such low temperatures, when practically all atoms are in
Bose-Einstein condensed state, which implies the broken global gauge symmetry.
Excitations are realized either by imposing external alternating fields,
modulating the trapping potential and shaking the cloud of trapped atoms, or it
can be done by varying atomic interactions by means of Feshbach resonance
techniques. Gradually increasing the amount of energy pumped into the system,
which is realized either by strengthening the modulation amplitude or by
increasing the excitation time, produces a series of nonequilibrium states,
with the growing fraction of atoms for which the gauge symmetry is restored. In
this way, the initial equilibrium system, with the broken gauge symmetry and
all atoms condensed, can be excited to the state, where all atoms are in the
normal state, with completely restored gauge symmetry. In this process, the
system, starting from the regular superfluid state, passes through the states
of vortex superfluid, turbulent superfluid, heterophase granular fluid, to the
state of normal chaotic fluid in turbulent regime. Both theoretical and
experimental studies are presented.Comment: Latex file, 25 pages, 4 figure