3,238 research outputs found
Stability of stationary states in the cubic nonlinear Schroedinger equation: applications to the Bose-Einstein condensate
The stability properties and perturbation-induced dynamics of the full set of
stationary states of the nonlinear Schroedinger equation are investigated
numerically in two physical contexts: periodic solutions on a ring and
confinement by a harmonic potential. Our comprehensive studies emphasize
physical interpretations useful to experimentalists. Perturbation by stochastic
white noise, phase engineering, and higher order nonlinearity are considered.
We treat both attractive and repulsive nonlinearity and illustrate the
soliton-train nature of the stationary states.Comment: 9 pages, 11 figure
Hyperkahler manifolds and nonabelian Hodge theory of (irregular) curves
Short survey based on talk given at the Institut Henri Poincare January 17th
2012, during program on surface groups. The aim was to describe some background
results before describing in detail (in subsequent talks) the results of
[Boa11c] related to wild character varieties and irregular mapping class
groups.Comment: 16 pages, 2 figures, 3 table
Third-order superintegrable systems separable in parabolic coordinates
In this paper, we investigate superintegrable systems which separate in
parabolic coordinates and admit a third-order integral of motion. We give the
corresponding determining equations and show that all such systems are
multi-separable and so admit two second-order integrals. The third-order
integral is their Lie or Poisson commutator. We discuss how this situation is
different from the Cartesian and polar cases where new potentials were
discovered which are not multi-separable and which are expressed in terms of
Painlev\'e transcendents or elliptic functions
Magnetolocalization in disordered quantum wires
The magnetic field dependent localization in a disordered quantum wire is
considered nonperturbatively.
An increase of an averaged localization length with the magnetic field is
found, saturating at twice its value without magnetic field.
The crossover behavior is shown to be governed both in the weak and strong
localization regime by the magnetic diffusion length L_B. This function is
derived analytically in closed form as a function of the ratio of the mean free
path l, the wire thickness W, and the magnetic length l_B for a two-dimensional
wire with specular boundary conditions, as well as for a parabolic wire. The
applicability of the analytical formulas to resistance measurements in the
strong localization regime is discussed. A comparison with recent experimental
results on magnetolocalization is included.Comment: 22 pages, RevTe
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