10,549 research outputs found
Nonlinear Evolution of the Magnetohydrodynamic Rayleigh-Taylor Instability
We study the nonlinear evolution of the magnetic Rayleigh-Taylor instability
using three-dimensional MHD simulations. We consider the idealized case of two
inviscid, perfectly conducting fluids of constant density separated by a
contact discontinuity perpendicular to the effective gravity g, with a uniform
magnetic field B parallel to the interface. Modes parallel to the field with
wavelengths smaller than l_c = [B B/(d_h - d_l) g] are suppressed (where d_h
and d_l are the densities of the heavy and light fluids respectively), whereas
modes perpendicular to B are unaffected. We study strong fields with l_c
varying between 0.01 and 0.36 of the horizontal extent of the computational
domain. Even a weak field produces tension forces on small scales that are
significant enough to reduce shear (as measured by the distribution of the
amplitude of vorticity), which in turn reduces the mixing between fluids, and
increases the rate at which bubbles and finger are displaced from the interface
compared to the purely hydrodynamic case. For strong fields, the highly
anisotropic nature of unstable modes produces ropes and filaments. However, at
late time flow along field lines produces large scale bubbles. The kinetic and
magnetic energies transverse to gravity remain in rough equipartition and
increase as t^4 at early times. The growth deviates from this form once the
magnetic energy in the vertical field becomes larger than the energy in the
initial field. We comment on the implications of our results to Z-pinch
experiments, and a variety of astrophysical systems.Comment: 25 pages, accepted by Physics of Fluids, online version of journal
has high resolution figure
Theory of the cold collision frequency shift in 1S--2S spectroscopy of Bose-Einstein-condensed and non-condensed hydrogen
We show that a correct formulation of the cold collision frequency shift for
two photon spectroscopy of Bose-condensed and cold non-Bose-condensed hydrogen
is consistent with experimental data. Our treatment includes transport and
inhomogeneity into the theory of a non-condensed gas, which causes substantial
changes in the cold collision frequency shift for the ordinary thermal gas, as
a result of the very high frequency (3.9kHz) of transverse trap mode. For the
condensed gas, we find substantial corrections arise from the inclusion of
quasiparticles, whose number is very large because of the very low frequency
(10.2Hz) of the longitudinal trap mode. These two effects together account for
the apparent absence of a "factor of two" between the two possibilities.
Our treatment considers only the Doppler-free measurements, but could be
extended to Doppler-sensitive measurements. For Bose-condensed hydrogen, we
predict a characteristic "foot" extending into higher detunings than can arise
from the condensate alone, as a result of a correct treatment of the statistics
of thermal quasiparticles.Comment: 16 page J Phys B format plus 6 postscript figure
The Quantum de Laval Nozzle: stability and quantum dynamics of sonic horizons in a toroidally trapped Bose gas containing a superflow
We study an experimentally realizable system containing stable black
hole-white hole acoustic horizons in toroidally trapped Bose-Einstein
condensates - the quantum de Laval nozzle. We numerically obtain stationary
flow configurations and assess their stability using Bogoliubov theory, finding
both in hydrodynamic and non-hydrodynamic regimes there exist dynamically
unstable regions associated with the creation of positive and negative energy
quasiparticle pairs in analogy with the gravitational Hawking effect. The
dynamical instability takes the form of a two mode squeezing interaction
between resonant pairs of Bogoliubov modes. We study the evolution of
dynamically unstable flows using the truncated Wigner method, which confirms
the two mode squeezed state picture of the analogue Hawking effect for low
winding number.Comment: 12 pages, 10 figure
Quadripartite continuous-variable entanglement via quadruply concurrent downconversion
We investigate an intra-cavity coupled down-conversion scheme to generate
quadripartite entanglement using concurrently resonant nonlinearities. We
verify that quadripartite entanglement is present in this system by calculating
the output fluctuation spectra and then considering violations of optimized
inequalities of the van Loock-Furusawa type. The entanglement characteristics
both above and below the oscillation threshold are considered. We also present
analytic solutions for the quadrature operators and the van Loock-Furusawa
correlations in the undepleted pump approximation.Comment: 9 pages, 5 figure
Theory of the Ramsey spectroscopy and anomalous segregation in ultra-cold rubidium
The recent anomalous segregation experiment of Lewandowski et al. (PRL, 88,
070403, 2002) shows dramatic, rapid internal state segregation for two
hyperfine levels of rubidium. We simulate an effective one dimensional model of
the system for experimental parameters and find reasonable agreement with the
data. The Ramsey frequency is found to be insensitive to the decoherence of the
superposition, and is only equivalent to the interaction energy shift for a
pure superposition. A Quantum Boltzmann equation describing collisions is
derived using Quantum Kinetic Theory, taking into account the different
scattering lengths of the internal states. As spin-wave experiments are likely
to be attempted at lower temperatures we examine the effect of degeneracy on
decoherence by considering the recent experiment of Lewandowski et al. where
degeneracy is around 10%. We also find that the segregation effect is only
possible when transport terms are included in the equations of motion, and that
the interactions only directly alter the momentum distributions of the states.
The segregation or spin wave effect is thus entirely due to coherent atomic
motion as foreseen in the experimental reportComment: 26 pages, 4 figures, to be published in J. Phys.
Properties of the stochastic Gross-Pitaevskii equation: Projected Ehrenfest relations and the optimal plane wave basis
We investigate the properties of the stochastic Gross-Pitaevskii equation
describing a condensate interacting with a stationary thermal cloud derived by
Gardiner and coworkers. We find the appropriate Ehrenfest relations for the
SGPE, including the effect of growth noise and projector terms arising from the
energy cutoff. This is carried out in the high temperature regime appropriate
for the SGPE, which simplifies the action of the projectors. The validity
condition for neglecting the projector terms in the Ehrenfest relations is
found to be more stringent than the usual condition of validity of the
truncated Wigner method or classical field method -- which is that all modes
are highly occupied. In addition it is required that the overlap of the
nonlinear term with the lowest energy eigenstate of the non-condensate band is
small. We show how to use the Ehrenfest relations along with the corrections
generated by the projector to monitor dynamical artifacts arising from the
cutoff. We also investigate the effect of using different bases to describe a
harmonically trapped BEC at finite temperature by comparing the condensate
fraction found using the plane wave and single particle bases. We show that the
equilibrium properties are strongly dependent on the choice of basis. There is
thus an optimal choice of plane wave basis for a given cut-off energy and we
show that this basis gives the best reproduction of the single particle
spectrum, the condensate fraction and the position and momentum densities.Comment: 23 pages, 5 figure
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