671 research outputs found
Symmetry breaking induced by random fluctuations for Bose-Einstein condensates in a double-well trap
This paper is devoted to the study of the dynamics of two weakly-coupled
Bose-Einstein condensates confined in a double-well trap and perturbed by
random external forces. Energy diffusion due to random forcing allows the
system to visit symmetry-breaking states when the number of atoms exceeds a
threshold value. The energy distribution evolves to a stationary distribution
which depends on the initial state of the condensate only through the total
number of atoms. This loss of memory of the initial conditions allows a simple
and complete description of the stationary dynamics of the condensate which
randomly visits symmetric and symmetry-breaking states.Comment: 12 pages, 6 figure
Orlicz Spaces associated with a Semi-Finite Von Neumann Algebra
In the present paper we introduce a certain class of non commutative Orlicz
spaces, associated with arbitrary faithful normal locally-finite weights on a
semi-finite von Neumann algebra We describe the dual spaces for such
Orlicz spaces and, in the case of regular weights, we show that they can be
realized as linear subspaces of the algebra of of locally measurable
operators affiliated with Comment: 12 page
Controlling collapse in Bose-Einstein condensates by temporal modulation of the scattering length
We consider, by means of the variational approximation (VA) and direct
numerical simulations of the Gross-Pitaevskii (GP) equation, the dynamics of 2D
and 3D condensates with a scattering length containing constant and
harmonically varying parts, which can be achieved with an ac magnetic field
tuned to the Feshbach resonance. For a rapid time modulation, we develop an
approach based on the direct averaging of the GP equation,without using the VA.
In the 2D case, both VA and direct simulations, as well as the averaging
method, reveal the existence of stable self-confined condensates without an
external trap, in agreement with qualitatively similar results recently
reported for spatial solitons in nonlinear optics. In the 3D case, the VA again
predicts the existence of a stable self-confined condensate without a trap. In
this case, direct simulations demonstrate that the stability is limited in
time, eventually switching into collapse, even though the constant part of the
scattering length is positive (but not too large). Thus a spatially uniform ac
magnetic field, resonantly tuned to control the scattering length, may play the
role of an effective trap confining the condensate, and sometimes causing its
collapse.Comment: 7 figure
Nonlinear localized modes in dipolar Bose-Einstein condensates in optical lattices
The modulational instability and discrete matter wave solitons in dipolar
BEC, loaded into a deep optical lattice, are investigated analytically and
numerically. The process of modulational instability of nonlinear plane matter
waves in a dipolar nonlinear lattice is studied and the regions of instability
are established. The existence and stability of bulk discrete solitons are
analyzed analytically and confirmed by numerical simulations. In a marked
contrast with the usual DNLS behavior (no dipolar interactions), we found a
region where the two fundamental modes are simultaneously unstable allowing
enhanced mobility across the lattice for large norm values. To study the
existence and properties of surface discrete solitons, an analysis of the dimer
configuration is performed. The properties of symmetric and antisymmetric modes
including the stability diagrams and bifurcations are investigated in closed
form. For the case of a bulk medium, properties of fundamental on-site and
inter-site localized modes are analyzed. On-site and inter-site surface
localized modes are studied finding that they do not exist when nonlocal
interactions predominate with respect to local ones.Comment: 12 pages, 13 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
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 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
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