81 research outputs found
Single vortex states in a confined Bose-Einstein condensate
It has been demonstrated experimentally that non-axially symmetric vortices
precess around the centre of a Bose-Einstein condensate. Two types of single
vortex states have been observed, usually referred to as the S-vortex and the
U-vortex. We study theoretically the single vortex excitations in spherical and
elongated condensates as a function of the interaction strength. We solve
numerically the Gross-Pitaevskii equation and calculate the angular momentum as
a function of precession frequency. The existence of two types of vortices
means that we have two different precession frequencies for each angular
momentum value. As the interaction strength increases the vortex lines bend and
the precession frequencies shift to lower values. We establish that for given
angular momentum the S-vortex has higher energy than the U-vortex in a rotating
elongated condensate. We show that the S-vortex is related to the solitonic
vortex which is a nonlinear excitation in the nonrotating system. For small
interaction strengths the S-vortex is related to the dark soliton. In the
dilute limit a lowest Landau level calculation provides an analytic description
of these vortex modes in terms of the harmonic oscillator states
Virial theorems for vortex states in a confined Bose-Einstein condensate
We derive a class of virial theorems which provide stringent tests of both
analytical and numerical calculations of vortex states in a confined
Bose-Einstein condensate. In the special case of harmonic confinement we arrive
at the somewhat surprising conclusion that the linear moments of the particle
density, as well as the linear momentum, must vanish even in the presence of
off-center vortices which lack axial or reflection symmetry. Illustrations are
provided by some analytical results in the limit of a dilute gas, and by a
numerical calculation of a class of single and double vortices at intermediate
couplings. The effect of anharmonic confinement is also discussed
Scattering of vortex pairs in 2D easy-plane ferromagnets
Vortex-antivortex pairs in 2D easy-plane ferromagnets have characteristics of
solitons in two dimensions. We investigate numerically and analytically the
dynamics of such vortex pairs. In particular we simulate numerically the
head-on collision of two pairs with different velocities for a wide range of
the total linear momentum of the system. If the momentum difference of the two
pairs is small, the vortices exchange partners, scatter at an angle depending
on this difference, and form two new identical pairs. If it is large, the pairs
pass through each other without losing their identity. We also study head-tail
collisions. Two identical pairs moving in the same direction are bound into a
moving quadrupole in which the two vortices as well as the two antivortices
rotate around each other. We study the scattering processes also analytically
in the frame of a collective variable theory, where the equations of motion for
a system of four vortices constitute an integrable system. The features of the
different collision scenarios are fully reproduced by the theory. We finally
compare some aspects of the present soliton scattering with the corresponding
situation in one dimension.Comment: 13 pages (RevTeX), 8 figure
Absence of Wavepacket Diffusion in Disordered Nonlinear Systems
We study the spreading of an initially localized wavepacket in two nonlinear
chains (discrete nonlinear Schroedinger and quartic Klein-Gordon) with
disorder. Previous studies suggest that there are many initial conditions such
that the second moment of the norm and energy density distributions diverge as
a function of time. We find that the participation number of a wavepacket does
not diverge simultaneously. We prove this result analytically for
norm-conserving models and strong enough nonlinearity. After long times the
dynamical state consists of a distribution of nondecaying yet interacting
normal modes. The Fourier spectrum shows quasiperiodic dynamics. Assuming this
result holds for any initially localized wavepacket, a limit profile for the
norm/energy distribution with infinite second moment should exist in all cases
which rules out the possibility of slow energy diffusion (subdiffusion). This
limit profile could be a quasiperiodic solution (KAM torus)
Solitons, solitonic vortices, and vortex rings in a confined Bose-Einstein condensate
Quasi-one-dimensional solitons that may occur in an elongated Bose-Einstein
condensate become unstable at high particle density. We study two basic modes
of instability and the corresponding bifurcations to genuinely
three-dimensional solitary waves such as axisymmetric vortex rings and
non-axisymmetric solitonic vortices. We calculate the profiles of the above
structures and examine their dependence on the velocity of propagation along a
cylindrical trap. At sufficiently high velocity, both the vortex ring and the
solitonic vortex transform into an axisymmetric soliton. We also calculate the
energy-momentum dispersions and show that a Lieb-type mode appears in the
excitation spectrum for all particle densities.Comment: RevTeX 9 pages, 9 figure
Scattering of magnetic solitons in two dimensions
Solitons which have the form of a vortex-antivortex pair have recently been
found in the Landau-Lifshitz equation which is the standard model for the
ferromagnet. We simulate numerically head-on collisions of two
vortex-antivortex pairs and observe a right angle scattering pattern. We offer
a resolution of this highly nontrivial dynamical behavior by examining the
Hamiltonian structure of the model, specifically the linear momentum of the two
solitons. We further investigate the dynamics of vortices in a modified
nonlinear sigma-model which arises in the description of antiferromagnets. We
confirm numerically that a robust feature of the dynamics is the right angle
scattering of two vortices which collide head-on. A generalization of our
theory is given for this model which offers arguments towards an understanding
of the observed dynamical behavior.Comment: 10 pages RevTeX, 9 figure
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