269 research outputs found
Low energy dynamics of spinor condensates
We present a derivation of the low energy Lagrangian governing the dynamics
of the spin degrees of freedom in a spinor Bose condensate, for any phase in
which the average magnetization vanishes. This includes all phases found within
mean-field treatments except for the ferromagnet, for which the low energy
dynamics has been discussed previously. The Lagrangian takes the form of a
sigma model for the rotation matrix describing the local orientation of the
spin state of the gas
Nothing but Relativity, Redux
Here we show how spacetime transformations consistent with the principle of
relativity can be derived without an explicit assumption of the constancy of
the speed of light, without gedanken experiments involving light rays, and
without an assumption of differentiability, or even continuity, for the
spacetime mapping. Hence, these historic results could have been derived
centuries ago, even before the advent of calculus. This raises an interesting
question: Could Galileo have derived Einsteinian relativity
Formation and evolution of density singularities in hydrodynamics of inelastic gases
We use ideal hydrodynamics to investigate clustering in a gas of
inelastically colliding spheres. The hydrodynamic equations exhibit a new type
of finite-time density blowup, where the gas pressure remains finite. The
density blowups signal formation of close-packed clusters. The blowup dynamics
are universal and describable by exact analytic solutions continuable beyond
the blowup time. These solutions show that dilute hydrodynamic equations yield
a powerful effective description of a granular gas flow with close-packed
clusters, described as finite-mass point-like singularities of the density.
This description is similar in spirit to the description of shocks in ordinary
ideal gas dynamics.Comment: 4 pages, 3 figures, final versio
Towards higher order lattice Boltzmann schemes
In this contribution we extend the Taylor expansion method proposed
previously by one of us and establish equivalent partial differential equations
of DDH lattice Boltzmann scheme at an arbitrary order of accuracy. We derive
formally the associated dynamical equations for classical thermal and linear
fluid models in one to three space dimensions. We use this approach to adjust
relaxation parameters in order to enforce fourth order accuracy for thermal
model and diffusive relaxation modes of the Stokes problem. We apply the
resulting scheme for numerical computation of associated eigenmodes and compare
our results with analytical references
Linearized model Fokker-Planck collision operators for gyrokinetic simulations. II. Numerical implementation and tests
A set of key properties for an ideal dissipation scheme in gyrokinetic
simulations is proposed, and implementation of a model collision operator
satisfying these properties is described. This operator is based on the exact
linearized test-particle collision operator, with approximations to the
field-particle terms that preserve conservation laws and an H-Theorem. It
includes energy diffusion, pitch-angle scattering, and finite Larmor radius
effects corresponding to classical (real-space) diffusion. The numerical
implementation in the continuum gyrokinetic code GS2 is fully implicit and
guarantees exact satisfaction of conservation properties. Numerical results are
presented showing that the correct physics is captured over the entire range of
collisionalities, from the collisionless to the strongly collisional regimes,
without recourse to artificial dissipation.Comment: 13 pages, 8 figures, submitted to Physics of Plasmas; typos fixe
Generation of nonground-state Bose-Einstein condensates by modulating atomic interactions
A technique is proposed for creating nonground-state Bose-Einstein
condensates in a trapping potential by means of the temporal modulation of
atomic interactions. Applying a time-dependent spatially homogeneous magnetic
field modifies the atomic scattering length. An alternating modulation of the
scattering length excites the condensate, which, under special conditions, can
be transferred to an excited nonlinear coherent mode. It is shown that there
occurs a phase-transition-like behavior in the time-averaged population
imbalance between the ground and excited states. The application of the
suggested technique to realistic experimental conditions is analyzed and it is
shown that the considered effect can be realized for experimentally available
condensates.Comment: 6 pages, 2 figures, 1 tabl
Relationships between various characterisations of wave tails
One can define several properties of wave equations that correspond to the
absence of tails in their solutions, the most common one by far being Huygens'
principle. Not all of these definitions are equivalent, although they are
sometimes assumed to be. We analyse this issue in detail for linear scalar
waves, establishing some relationships between the various properties. Huygens'
principle is almost always equivalent to the characteristic propagation
property, and in two spacetime dimensions the latter is equivalent to the
zeroth order progressing wave propagation property. Higher order progressing
waves in general do have tails, and do not seem to admit a simple physical
characterisation, but they are nevertheless useful because of their close
association with exactly solvable two-dimensional equations.Comment: Plain TeX, 26 page
The Effect of Neutral Atoms on Capillary Discharge Z-pinch
We study the effect of neutral atoms on the dynamics of a capillary discharge
Z-pinch, in a regime for which a large soft-x-ray amplification has been
demonstrated. We extended the commonly used one-fluid magneto-hydrodynamics
(MHD) model by separating out the neutral atoms as a second fluid. Numerical
calculations using this extended model yield new predictions for the dynamics
of the pinch collapse, and better agreement with known measured data.Comment: 4 pages, 4 postscript figures, to be published in Phys. Rev. Let
Antisymmetrized Green's function approach to reactions with a realistic nuclear density
A completely antisymmetrized Green's function approach to the inclusive
quasielastic scattering, including a realistic one-body density, is
presented. The single particle Green's function is expanded in terms of the
eigenfunctions of the nonhermitian optical potential. This allows one to treat
final state interactions consistently in the inclusive and in the exclusive
reactions. Nuclear correlations are included in the one-body density. Numerical
results for the response functions of O and Ca are presented and
discussed.Comment: 45 pages, 3 figure
Derivation of the Blackbody Radiation Spectrum from a Natural Maximum-Entropy Principle Involving Casimir Energies and Zero-Point Radiation
By numerical calculation, the Planck spectrum with zero-point radiation is
shown to satisfy a natural maximum-entropy principle whereas alternative
choices of spectra do not. Specifically, if we consider a set of
conducting-walled boxes, each with a partition placed at a different location
in the box, so that across the collection of boxes the partitions are uniformly
spaced across the volume, then the Planck spectrum correspond to that spectrum
of random radiation (having constant energy kT per normal mode at low
frequencies and zero-point energy (1/2)hw per normal mode at high frequencies)
which gives maximum uniformity across the collection of boxes for the radiation
energy per box. The analysis involves Casimir energies and zero-point radiation
which do not usually appear in thermodynamic analyses. For simplicity, the
analysis is presented for waves in one space dimension.Comment: 11 page
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