5,970 research outputs found
Dark matter-wave solitons in the dimensionality crossover
We consider the statics and dynamics of dark matter-wave solitons in the
dimensionality crossover regime from 3D to 1D. There, using the nonpolynomial
Schr\"{o}dinger mean-field model, we find that the anomalous mode of the
Bogoliubov spectrum has an eigenfrequency which coincides with the soliton
oscillation frequency obtained by the 3D Gross-Pitaevskii model. We show that
substantial deviations (of order of 10% or more) from the characteristic
frequency ( being the longitudinal trap
frequency) are possible even in the purely 1D regime.Comment: Phys. Rev. A, in pres
Backlund transformations for the sl(2) Gaudin magnet
Elementary, one- and two-point, Backlund transformations are constructed for
the generic case of the sl(2) Gaudin magnet. The spectrality property is used
to construct these explicitly given, Poisson integrable maps which are
time-discretizations of the continuous flows with any Hamiltonian from the
spectral curve of the 2x2 Lax matrix.Comment: 17 pages, LaTeX, refs adde
Formation of singularities on the surface of a liquid metal in a strong electric field
The nonlinear dynamics of the free surface of an ideal conducting liquid in a
strong external electric field is studied. It is establish that the equations
of motion for such a liquid can be solved in the approximation in which the
surface deviates from a plane by small angles. This makes it possible to show
that on an initially smooth surface for almost any initial conditions points
with an infinite curvature corresponding to branch points of the root type can
form in a finite time.Comment: 14 page
New boundary conditions for integrable lattices
New boundary conditions for integrable nonlinear lattices of the XXX type,
such as the Heisenberg chain and the Toda lattice are presented. These
integrable extensions are formulated in terms of a generic XXX Heisenberg
magnet interacting with two additional spins at each end of the chain. The
construction uses the most general rank 1 ansatz for the 2x2 L-operator
satisfying the reflection equation algebra with rational r-matrix. The
associated quadratic algebra is shown to be the one of dynamical symmetry for
the A1 and BC2 Calogero-Moser problems. Other physical realizations of our
quadratic algebra are also considered.Comment: 22 pages, latex, no figure
Relaxation of nonlinear oscillations in BCS superconductivity
The diagonal case of the Richardson-Gaudin quantum pairing model
\cite{Richardson1,Richardson2,Richardson3,Richardson4,Richardson5,Richardson6,G
audin76} is known to be solvable as an Abel-Jacobi inversion problem
\cite{SOV,Kuznetzov,Kuz1,Kuz2,Kuz3,Kuz4,Kuz5,YAKE04}. This is an isospectral
(stationary) solution to a more general integrable hierarchy, in which the full
time evolution can be written as isomonodromic deformations. Physically, the
more general solution is appropriate when the single-particle electronic
spectrum is subject to external perturbations. The asymptotic behavior of the
nonlinear oscillations in the case of elliptic solutions is derived
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