8,779 research outputs found
Statistical kinetic treatment of relativistic binary collisions
In particle-based algorithms, the effect of binary collisions is commonly
described in a statistical way, using Monte Carlo techniques. It is shown that,
in the relativistic regime, stringent constraints should be considered on the
sampling of particle pairs for collision, which are critical to ensure
physically meaningful results, and that nonrelativistic sampling criteria
(e.g., uniform random pairing) yield qualitatively wrong results, including
equilibrium distributions that differ from the theoretical J\"uttner
distribution. A general procedure for relativistically consistent algorithms is
provided, and verified with three-dimensional Monte Carlo simulations, thus
opening the way to the numerical exploration of the statistical properties of
collisional relativistic systems.Comment: Accepted for publication as a Rapid Communication in Phys. Rev.
Poisson-Bracket Approach to the Dynamics of Nematic Liquid Crystals. The Role of Spin Angular Momentum
Nematic liquid crystals are well modeled as a fluid of rigid rods. Starting
from this model, we use a Poisson-bracket formalism to derive the equations
governing the dynamics of nematic liquid crystals. We treat the spin angular
momentum density arising from the rotation of constituent molecules about their
centers of mass as an independent field and derive equations for it, the mass
density, the momentum density, and the nematic director. Our equations reduce
to the original Leslie-Ericksen equations, including the inertial director term
that is neglected in the hydrodynamic limit, only when the moment of inertia
for angular momentum parallel to the director vanishes and when a dissipative
coefficient favoring locking of the angular frequencies of director rotation
and spin angular momentum diverges. Our equations reduce to the equations of
nematohydrodynamics in the hydrodynamic limit but with dissipative coefficients
that depend on the coefficient that must diverge to produce the Leslie-Ericksen
equations.Comment: 10 pages, to be published in Phys. Rev. E 72(5
Momentum of an electromagnetic wave in dielectric media
Almost a hundred years ago, two different expressions were proposed for the
energy--momentum tensor of an electromagnetic wave in a dielectric. Minkowski's
tensor predicted an increase in the linear momentum of the wave on entering a
dielectric medium, whereas Abraham's tensor predicted its decrease. Theoretical
arguments were advanced in favour of both sides, and experiments proved
incapable of distinguishing between the two. Yet more forms were proposed, each
with their advocates who considered the form that they were proposing to be the
one true tensor. This paper reviews the debate and its eventual conclusion:
that no electromagnetic wave energy--momentum tensor is complete on its own.
When the appropriate accompanying energy--momentum tensor for the material
medium is also considered, experimental predictions of all the various proposed
tensors will always be the same, and the preferred form is therefore
effectively a matter of personal choice.Comment: 23 pages, 3 figures, RevTeX 4. Removed erroneous factor of mu/mu_0
from Eq.(44
Heat Capacity and Magnetic Phase Diagram of the Low-Dimensional Antiferromagnet YBaCuO
A study by specific heat of a polycrystalline sample of the low-dimensional
magnetic system YBaCuO is presented. Magnetic fields up to 14 T are
applied and permit to extract the (,) phase diagram. Below
T, the N\'eel temperature, associated with a
three-dimensional antiferromagnetic long-range ordering, is constant and equals
K. Above , increases linearly with and a
field-induced increase of the entropy at is related to the presence of an
isosbestic point at K, where all the specific heat curves cross.
A comparison is made between YBaCuO and the quasi-two-dimensional
magnetic systems BaNiVO, SrCuOCl, and
PrCuO, for which very similar phase diagrams have been reported. An
effective field-induced magnetic anisotropy is proposed to explain these phase
diagrams.Comment: 14 pages, 7 figure
Statistical mechanics in the context of special relativity II
The special relativity laws emerge as one-parameter (light speed)
generalizations of the corresponding laws of classical physics. These
generalizations, imposed by the Lorentz transformations, affect both the
definition of the various physical observables (e.g. momentum, energy, etc), as
well as the mathematical apparatus of the theory. Here, following the general
lines of [Phys. Rev. E {\bf 66}, 056125 (2002)], we show that the Lorentz
transformations impose also a proper one-parameter generalization of the
classical Boltzmann-Gibbs-Shannon entropy. The obtained relativistic entropy
permits to construct a coherent and selfconsistent relativistic statistical
theory, preserving the main features of the ordinary statistical theory, which
recovers in the classical limit. The predicted distribution function is a
one-parameter continuous deformation of the classical Maxwell-Boltzmann
distribution and has a simple analytic form, showing power law tails in
accordance with the experimental evidence. Furthermore the new statistical
mechanics can be obtained as stationary case of a generalized kinetic theory
governed by an evolution equation obeying the H-theorem and reproducing the
Boltzmann equation of the ordinary kinetics in the classical limit.Comment: 14 pages, no figures, proof correction
Dynamical approach to the Casimir effect
Casimir forces can appear between intrusions placed in different media driven
by several fluctuation mechanisms, either in equilibrium or out of it. Herein,
we develop a general formalism to obtain such forces from the dynamical
equations of the fluctuating medium, the statistical properties of the driving
noise, and the boundary conditions of the intrusions (which simulate the
interaction between the intrusions and the medium). As a result, an explicit
formula for the Casimir force over the intrusions is derived. This formalism
contains the thermal Casimir effect as a particular limit and generalizes the
study of the Casimir effect to such systems through their dynamical equations,
with no appeal to their Hamiltonian, if any exists. In particular, we study the
Casimir force between two infinite parallel plates with Dirichlet or Neumann
boundary conditions, immersed in several media with finite correlation lengths
(reaction--diffusion system, liquid crystals, and two coupled fields with
non-Hermitian evolution equations). The driving Gaussian noises have vanishing
or finite spatial or temporal correlation lengths; in the first case,
equilibrium is reobtained and finite correlations produce nonequilibrium
dynamics. The results obtained show that, generally, nonequilibrium dynamics
leads to Casimir forces, whereas Casimir forces are obtained in equilibrium
dynamics if the stress tensor is anisotropic.Comment: 12 pages, 1 figur
Canonical and kinetic forms of the electromagnetic momentum in an ad hoc quantization scheme for a dispersive dielectric
An ad hoc quantization scheme for the electromagnetic field in a weakly
dispersive, transparent dielectric leads to the definition of canonical and
kinetic forms for the momentum of the electromagnetic field in a dispersive
medium. The canonical momentum is uniquely defined as the operator that
generates spatial translations in a uniform medium, but the quantization scheme
suggests two possible choices for the kinetic momentum operator, corresponding
to the Abraham or the Minkowski momentum in classical electrodynamics. Another
implication of this procedure is that a wave packet containing a single dressed
photon travels at the group velocity through the medium. The physical
significance of the canonical momentum has already been established by
considerations of energy and momentum conservation in the atomic recoil due to
spontaneous emission, the Cerenkov effect, the Doppler effect, and phase
matching in nonlinear optical processes. In addition, the data of the Jones and
Leslie radiation pressure experiment is consistent with the assignment of one
?k unit of canonical momentum to each dressed photon. By contrast, experiments
in which the dielectric is rigidly accelerated by unbalanced electromagnetic
forces require the use of the Abraham momentum.Comment: 21 pages, 1 figure, aip style, submitted to PR
Direct observation of electron doping in La0.7Ce0.3MnO3 using x-ray absorption spectroscopy
We report on a X-ray absorption spectroscopic (XAS) study on a thin film of
La0.7Ce0.3MnO3, a manganite which was previously only speculated to be an
electron doped system. The measurements clearly show that the cerium is in the
Ce(IV) valence state and that the manganese is present in a mixture of Mn2+ and
Mn3+ valence states. These data unambiguously demonstrate that La0.7Ce0.3MnO3
is an electron doped colossal magnetoresistive manganite, a finding that may
open up new opportunities both for device applications as well as for further
basic research towards a better modelling of the colossal magnetoresistance
phenomenon in these materials.Comment: 4 pages, 3 figures, revised versio
Relativistic Viscous Fluid Dynamics and Non-Equilibrium Entropy
Fluid dynamics corresponds to the dynamics of a substance in the long
wavelength limit. Writing down all terms in a gradient (long wavelength)
expansion up to second order for a relativistic system at vanishing charge
density, one obtains the most general (causal) equations of motion for a fluid
in the presence of shear and bulk viscosity, as well as the structure of the
non-equilibrium entropy current. Requiring positivity of the divergence of the
non-equilibrium entropy current relates some of its coefficients to those
entering the equations of motion. I comment on possible applications of these
results for conformal and non-conformal fluids.Comment: 25 pages, no figures; v2: matches published versio
Thermodynamically admissible form for discrete hydrodynamics
We construct a discrete model of fluid particles according to the GENERIC
formalism. The model has the form of Smoothed Particle Hydrodynamics including
correct thermal fluctuations. A slight variation of the model reproduces the
Dissipative Particle Dynamics model with any desired thermodynamic behavior.
The resulting algorithm has the following properties: mass, momentum and energy
are conserved, entropy is a non-decreasing function of time and the thermal
fluctuations produce the correct Einstein distribution function at equilibrium.Comment: 4 page
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