463 research outputs found
Scarring in a driven system with wave chaos
We consider acoustic wave propagation in a model of a deep ocean acoustic
waveguide with a periodic range-dependence. Formally, the wave field is
described by the Schrodinger equation with a time-dependent Hamiltonian. Using
methods borrowed from the quantum chaos theory it is shown that in the driven
system under consideration there exists a "scarring" effect similar to that
observed in autonomous quantum systems.Comment: 5 pages, 7 figure
Compactons in Nonlinear Schr\"odinger Lattices with Strong Nonlinearity Management
The existence of compactons in the discrete nonlinear Schr\"odinger equation
in the presence of fast periodic time modulations of the nonlinearity is
demonstrated. In the averaged DNLS equation the resulting effective inter-well
tunneling depends on modulation parameters {\it and} on the field amplitude.
This introduces nonlinear dispersion in the system and can lead to a
prototypical realization of single- or multi-site stable discrete compactons in
nonlinear optical waveguide and BEC arrays. These structures can dynamically
arise out of Gaussian or compactly supported initial data.Comment: 4 pages, 4 figure
The frustrated Brownian motion of nonlocal solitary waves
We investigate the evolution of solitary waves in a nonlocal medium in the
presence of disorder. By using a perturbational approach, we show that an
increasing degree of nonlocality may largely hamper the Brownian motion of
self-trapped wave-packets. The result is valid for any kind of nonlocality and
in the presence of non-paraxial effects. Analytical predictions are compared
with numerical simulations based on stochastic partial differential equationComment: 4 pages, 3 figures
Collapse of a Bose-Einstein condensate induced by fluctuations of the laser intensity
The dynamics of a metastable attractive Bose-Einstein condensate trapped by a
system of laser beams is analyzed in the presence of small fluctuations of the
laser intensity. It is shown that the condensate will eventually collapse. The
expected collapse time is inversely proportional to the integrated covariance
of the time autocorrelation function of the laser intensity and it decays
logarithmically with the number of atoms. Numerical simulations of the
stochastic 3D Gross-Pitaevskii equation confirms analytical predictions for
small and moderate values of mean field interaction.Comment: 13 pages, 7 eps figure
Solitons in Tonks-Girardeau gas with dipolar interactions
The existence of bright solitons in the model of the Tonks-Girardeau (TG) gas
with dipole-dipole (DD) interactions is reported. The governing equation is
taken as the quintic nonlinear Schr\"{o}dinger equation (NLSE) with the
nonlocal cubic term accounting for the DD attraction. In different regions of
the parameter space (the dipole moment and atom number), matter-wave solitons
feature flat-top or compacton-like shapes. For the flat-top states, the NLSE
with the local cubic-quintic (CQ) nonlinearity is shown to be a good
approximation. Specific dynamical effects are studied assuming that the
strength of the DD interactions is ramped up or drops to zero. Generation of
dark-soliton pairs in the gas shrinking under the action of the intensifying DD
attraction is observed. Dark solitons exhibit the particle-like collision
behavior. Peculiarities of dipole solitons in the TG gas are highlighted by
comparison with the NLSE including the local CQ terms. Collisions between the
solitons are studied too. In many cases, the collisions result in merger of the
solitons into a breather, due to strong attraction between them.Comment: 15 pages, 8 figures, accepted by J. Phys. B: At. Mol. Opt. Phy
Modulational and Parametric Instabilities of the Discrete Nonlinear Schr\"odinger Equation
We examine the modulational and parametric instabilities arising in a
non-autonomous, discrete nonlinear Schr{\"o}dinger equation setting. The
principal motivation for our study stems from the dynamics of Bose-Einstein
condensates trapped in a deep optical lattice. We find that under periodic
variations of the heights of the interwell barriers (or equivalently of the
scattering length), additionally to the modulational instability, a window of
parametric instability becomes available to the system. We explore this
instability through multiple-scale analysis and identify it numerically. Its
principal dynamical characteristic is that, typically, it develops over much
larger times than the modulational instability, a feature that is qualitatively
justified by comparison of the corresponding instability growth rates
Collapse and revival of oscillations in a parametrically excited Bose-Einstein condensate in combined harmonic and optical lattice trap
In this work, we study parametric resonances in an elongated cigar-shaped BEC
in a combined harmonic trap and a time dependent optical lattice by using
numerical and analytical techniques. We show that there exists a relative
competition between the harmonic trap which tries to spatially localize the BEC
and the time varying optical lattice which tries to delocalize the BEC. This
competition gives rise to parametric resonances (collapse and revival of the
oscillations of the BEC width). Parametric resonances disappear when one of the
competing factors i.e strength of harmonic trap or the strength of optical
lattice dominates. Parametric instabilities (exponential growth of Bogoliubov
modes) arise for large variations in the strength of the optical lattice.Comment: 9 pages, 20 figure
Theory of Nonlinear Dispersive Waves and Selection of the Ground State
A theory of time dependent nonlinear dispersive equations of the Schroedinger
/ Gross-Pitaevskii and Hartree type is developed. The short, intermediate and
large time behavior is found, by deriving nonlinear Master equations (NLME),
governing the evolution of the mode powers, and by a novel multi-time scale
analysis of these equations. The scattering theory is developed and coherent
resonance phenomena and associated lifetimes are derived. Applications include
BEC large time dynamics and nonlinear optical systems. The theory reveals a
nonlinear transition phenomenon, ``selection of the ground state'', and NLME
predicts the decay of excited state, with half its energy transferred to the
ground state and half to radiation modes. Our results predict the recent
experimental observations of Mandelik et. al. in nonlinear optical waveguides
Above-bandgap ordinary optical properties of GaSe single crystal
We report above-bandgap ordinary optical properties of ε-phase GaSe single crystal. Reference-quality pseudodielectric function 〈ε(E)〉 = 〈ε1(E)〉+i〈ε2(E)〉 and pseudorefractive index 〈N(E)〉 = 〈n(E)〉+i〈k(E)〉 spectra were measured by spectroscopic ellipsometry from 0.73 to 6.45 eV at room temperature for the light polarization perpendicular to the optic axis (math⊥math). The 〈ε〉 spectrum exhibited several interband-transition critical-point structures. Analysis of second-energy derivatives calculated numerically from the measured data yielded the critical-point energy [email protected]
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