6,690 research outputs found
Flux-corrected transport techniques for transient calculations of strongly shocked flows
New flux-corrected transport algorithms are described for solving generalized continuity equations. These techniques were developed by requiring that the finite difference formulas used ensure positivity for an initially positive convected quantity. Thus FCT is particularly valuable for fluid-like problems with strong gradients or shocks. Repeated application of the same subroutine to mass, momentum, and energy conservation equations gives a simple solution of the coupled time-dependent equations of ideal compressible fluid dynamics without introducing an artificial viscosity. FCT algorithms span Eulerian, sliding-rezone, and Lagrangian finite difference grids in several coordinate systems. The latest FCT techniques are fully vectorized for parallel/pipeline processing
Typical state of an isolated quantum system with fixed energy and unrestricted participation of eigenstates
This work describes the statistics for the occupation numbers of quantum
levels in a large isolated quantum system, where all possible superpositions of
eigenstates are allowed, provided all these superpositions have the same fixed
energy. Such a condition is not equivalent to the conventional micro-canonical
condition, because the latter limits the participating eigenstates to a very
narrow energy window. The statistics is obtained analytically for both the
entire system and its small subsystem. In a significant departure from the
Boltzmann-Gibbs statistics, the average occupation numbers of quantum states
exhibit in the present case weak algebraic dependence on energy. In the
macroscopic limit, this dependence is routinely accompanied by the condensation
into the lowest energy quantum state. This work contains initial numerical
tests of the above statistics for finite systems, and also reports the
following numerical finding: When the basis states of large but finite random
matrix Hamiltonians are expanded in terms of eigenstates, the participation of
eigenstates in such an expansion obeys the newly obtained statistics. The above
statistics might be observable in small quantum systems, but for the
macroscopic systems, it rather reenforces doubts about self-sufficiency of
non-relativistic quantum mechanics for justifying the Boltzmann-Gibbs
equilibrium.Comment: 20 pages, 3 figure
Modulated Amplitude Waves in Collisionally Inhomogeneous Bose-Einstein Condensates
We investigate the dynamics of an effectively one-dimensional Bose-Einstein
condensate (BEC) with scattering length subjected to a spatially periodic
modulation, . This "collisionally inhomogeneous" BEC is
described by a Gross-Pitaevskii (GP) equation whose nonlinearity coefficient is
a periodic function of . We transform this equation into a GP equation with
constant coefficient and an additional effective potential and study a
class of extended wave solutions of the transformed equation. For weak
underlying inhomogeneity, the effective potential takes a form resembling a
superlattice, and the amplitude dynamics of the solutions of the
constant-coefficient GP equation obey a nonlinear generalization of the Ince
equation. In the small-amplitude limit, we use averaging to construct
analytical solutions for modulated amplitude waves (MAWs), whose stability we
subsequently examine using both numerical simulations of the original GP
equation and fixed-point computations with the MAWs as numerically exact
solutions. We show that "on-site" solutions, whose maxima correspond to maxima
of , are significantly more stable than their "off-site" counterparts.Comment: 25 pages, 10 figures (many with several parts), to appear in Physica
D; higher resolution versions of some figures are available at
http://www.its.caltech.edu/~mason/paper
Static and rotating domain-wall crosses in Bose-Einstein condensates
For a Bose-Einstein condensate (BEC) in a two-dimensional (2D) trap, we
introduce cross patterns, which are generated by intersection of two domain
walls (DWs) separating immiscible species, with opposite signs of the wave
functions in each pair of sectors filled by the same species. The cross pattern
remains stable up to the zero value of the immiscibility parameter ,
while simpler rectilinear (quasi-1D) DWs exist only for values of
essentially exceeding those in BEC mixtures (two spin states of the same
isotope) currently available to the experiment. Both symmetric and asymmetric
cross configurations are investigated, with equal or different numbers
of atoms in the two species. In rotating traps, ``propellers''
(stable revolving crosses) are found too. A full stability region for of the
crosses and propellers in the system's parameter space is identified, unstable
crosses evolving into arrays of vortex-antivortex pairs. Stable rotating
rectilinear DWs are found too, at larger vlues of . All the patterns
produced by the intersection of three or more DWs are unstable, rearranging
themselves into ones with two DWs. Optical propellers are also predicted in a
twisted nonlinear photonic-crystal fiber carrying two different wavelengths or
circular polarizations, which can be used for applications to switching and
routing.Comment: 9 pages, 10 figures, Phys. Rev. A (in press
Effects of high energy photon emissions in laser generated ultra-relativistic plasmas: real-time synchrotron simulations
We model the emission of high energy photons due to relativistic charged
particle motion in intense laser-plasma interactions. This is done within a
particle-in-cell code, for which high frequency radiation normally cannot be
resolved due to finite time steps and grid size. A simple expression for the
synchrotron radiation spectra is used together with a Monte-Carlo method for
the emittance. We extend previous work by allowing for arbitrary fields,
considering the particles to be in instantaneous circular motion due to an
effective magnetic field. Furthermore we implement noise reduction techniques
and present validity estimates of the method. Finally, we perform a rigorous
comparison to the mechanism of radiation reaction, and find the emitted energy
to be in excellent agreement with the losses calculated using radiation
reaction
On the Supersolid State of Matter
We prove that the necessary condition for a solid to be also a superfluid is
to have zero-point vacancies, or interstitial atoms, or both, as an integral
part of the ground state. As a consequence, superfluidity is not possible in
commensurate solids which break continuous translation symmetry. We discuss
recent experiment by Kim and Chan [Nature, {\bf 427}, 225 (2004)] in the
context of this theorem, question its bulk supersolid interpretation, and offer
an alternative explanation in terms of superfluid helium interfaces.Comment: 4 figures, 4 page
Superfluidity within Exact Renormalisation Group approach
The application of the exact renormalisation group to a many-fermion system
with a short-range attractive force is studied. We assume a simple ansatz for
the effective action with effective bosons, describing pairing effects and
derive a set of approximate flow equations for the effective coupling including
boson and fermionic fluctuations.
The phase transition to a phase with broken symmetry is found at a critical
value of the running scale. The mean-field results are recovered if boson-loop
effects are omitted. The calculations with two different forms of the regulator
was shown to lead to similar results.Comment: 17 pages, 3 figures, to appear in the proceedings of Renormalization
Group 2005 (RG 2005), Helsinki, Finland, 30 Aug - 3 Sep 200
Families of Matter-Waves for Two-Component Bose-Einstein Condensates
We produce several families of solutions for two-component nonlinear
Schr\"{o}dinger/Gross-Pitaevskii equations. These include domain walls and the
first example of an antidark or gray soliton in the one component, bound to a
bright or dark soliton in the other. Most of these solutions are linearly
stable in their entire domain of existence. Some of them are relevant to
nonlinear optics, and all to Bose-Einstein condensates (BECs). In the latter
context, we demonstrate robustness of the structures in the presence of
parabolic and periodic potentials (corresponding, respectively, to the magnetic
trap and optical lattices in BECs).Comment: 6 pages, 4 figures, EPJD in pres
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