147 research outputs found
Pion gas viscosity at low temperature and density
By using Chiral Perturbation Theory and the Uehling-Uhlenbeck equation we
compute the viscosity of a pion gas, in the low temperature and low density
regime, in terms of the temperature, and the pion fugacity. The viscosity turns
out to be proportional to the squared root of the temperature over the pion
mass. Next to leading corrections are proportional to the temperature over the
pion mass to the 3/2.Comment: 15 pages, 4 figures. RevTeX
Nuclear Isospin Diffusivity
The isospin diffusion and other irreversible phenomena are discussed for a
two-component nuclear Fermi system. The set of Boltzmann transport equations,
such as employed for reactions, are linearized, for weak deviations of a system
from uniformity, in order to arrive at nonreversible fluxes linear in the
nonuniformities. Besides the diffusion driven by a concentration gradient, also
the diffusion driven by temperature and pressure gradients is considered.
Diffusivity, conductivity, heat conduction and shear viscosity coefficients are
formally expressed in terms of the responses of distribution functions to the
nonuniformities. The linearized Boltzmann-equation set is solved, under the
approximation of constant form-factors in the distribution-function responses,
to find concrete expressions for the transport coefficients in terms of
weighted collision integrals. The coefficients are calculated numerically for
nuclear matter, using experimental nucleon-nucleon cross sections. The isospin
diffusivity is inversely proportional to the neutron-proton cross section and
is also sensitive to the symmetry energy. At low temperatures in symmetric
matter, the diffusivity is directly proportional to the symmetry energy.Comment: 35 pages, 1 table, 5 figures, accepted by PRC, (v3) changes in
response to the referee's comments, discussion for isospin diffusion process
in heavy-ion reactions, fig. 5 shows results from a two different isospin
depndent uclear equation of state, and a new reference adde
Thermal Effects in Low-Temperature QED
QED is studied at low temperature (, where is the electron mass)
and zero chemical potential. By integrating out the electron field and the
nonzero bosonic Matsubara modes, we construct an effective three-dimensional
field theory that is valid at distances . As applications, we
reproduce the ring-improved free energy and calculate the Debye mass to order
.Comment: 20 pages, 4 figures, revte
Relaxation rates and collision integrals for Bose-Einstein condensates
Near equilibrium, the rate of relaxation to equilibrium and the transport
properties of excitations (bogolons) in a dilute Bose-Einstein condensate (BEC)
are determined by three collision integrals, ,
, and . All three collision integrals
conserve momentum and energy during bogolon collisions, but only conserves bogolon number. Previous works have considered the
contribution of only two collision integrals, and . In this work, we show that the third collision integral makes a significant contribution to the bogolon number
relaxation rate and needs to be retained when computing relaxation properties
of the BEC. We provide values of relaxation rates in a form that can be applied
to a variety of dilute Bose-Einstein condensates.Comment: 18 pages, 4 figures, accepted by Journal of Low Temperature Physics
7/201
Renormalization and asymptotic expansion of Dirac's polarized vacuum
We perform rigorously the charge renormalization of the so-called reduced
Bogoliubov-Dirac-Fock (rBDF) model. This nonlinear theory, based on the Dirac
operator, describes atoms and molecules while taking into account vacuum
polarization effects. We consider the total physical density including both the
external density of a nucleus and the self-consistent polarization of the Dirac
sea, but no `real' electron. We show that it admits an asymptotic expansion to
any order in powers of the physical coupling constant \alphaph, provided that
the ultraviolet cut-off behaves as \Lambda\sim e^{3\pi(1-Z_3)/2\alphaph}\gg1.
The renormalization parameter $
Self-consistent solution for the polarized vacuum in a no-photon QED model
We study the Bogoliubov-Dirac-Fock model introduced by Chaix and Iracane
({\it J. Phys. B.}, 22, 3791--3814, 1989) which is a mean-field theory deduced
from no-photon QED. The associated functional is bounded from below. In the
presence of an external field, a minimizer, if it exists, is interpreted as the
polarized vacuum and it solves a self-consistent equation.
In a recent paper math-ph/0403005, we proved the convergence of the iterative
fixed-point scheme naturally associated with this equation to a global
minimizer of the BDF functional, under some restrictive conditions on the
external potential, the ultraviolet cut-off and the bare fine
structure constant . In the present work, we improve this result by
showing the existence of the minimizer by a variational method, for any cut-off
and without any constraint on the external field.
We also study the behaviour of the minimizer as goes to infinity
and show that the theory is "nullified" in that limit, as predicted first by
Landau: the vacuum totally kills the external potential. Therefore the limit
case of an infinite cut-off makes no sense both from a physical and
mathematical point of view.
Finally, we perform a charge and density renormalization scheme applying
simultaneously to all orders of the fine structure constant , on a
simplified model where the exchange term is neglected.Comment: Final version, to appear in J. Phys. A: Math. Ge
Space-time versus particle-hole symmetry in quantum Enskog equations
The non-local scattering-in and -out integrals of the Enskog equation have
reversed displacements of colliding particles reflecting that the -in and -out
processes are conjugated by the space and time inversions. Generalisations of
the Enskog equation to Fermi liquid systems are hindered by a request of the
particle-hole symmetry which contradicts the reversed displacements. We resolve
this problem with the help of the optical theorem. It is found that space-time
and particle-hole symmetry can only be fulfilled simultaneously for the
Bruckner-type of internal Pauli-blocking while the Feynman-Galitskii form
allows only for particle-hole symmetry but not for space-time symmetry due to a
stimulated emission of Bosons
Existence of global-in-time solutions to a generalized Dirac-Fock type evolution equation
We consider a generalized Dirac-Fock type evolution equation deduced from
no-photon Quantum Electrodynamics, which describes the self-consistent
time-evolution of relativistic electrons, the observable ones as well as those
filling up the Dirac sea. This equation has been originally introduced by Dirac
in 1934 in a simplified form. Since we work in a Hartree-Fock type
approximation, the elements describing the physical state of the electrons are
infinite rank projectors. Using the Bogoliubov-Dirac-Fock formalism, introduced
by Chaix-Iracane ({\it J. Phys. B.}, 22, 3791--3814, 1989), and recently
established by Hainzl-Lewin-Sere, we prove the existence of global-in-time
solutions of the considered evolution equation.Comment: 12 pages; more explanations added, some final (minor) corrections
include
Quantum Kinetic Theory V: Quantum kinetic master equation for mutual interaction of condensate and noncondensate
A detailed quantum kinetic master equation is developed which couples the
kinetics of a trapped condensate to the vapor of non-condensed particles. This
generalizes previous work which treated the vapor as being undepleted.Comment: RevTeX, 26 pages and 5 eps figure
Generalized Boltzmann Equation in a Manifestly Covariant Relativistic Statistical Mechanics
We consider the relativistic statistical mechanics of an ensemble of
events with motion in space-time parametrized by an invariant ``historical
time'' We generalize the approach of Yang and Yao, based on the Wigner
distribution functions and the Bogoliubov hypotheses, to find the approximate
dynamical equation for the kinetic state of any nonequilibrium system to the
relativistic case, and obtain a manifestly covariant Boltzmann-type equation
which is a relativistic generalization of the Boltzmann-Uehling-Uhlenbeck (BUU)
equation for indistinguishable particles. This equation is then used to prove
the -theorem for evolution in In the equilibrium limit, the
covariant forms of the standard statistical mechanical distributions are
obtained. We introduce two-body interactions by means of the direct action
potential where is an invariant distance in the Minkowski
space-time. The two-body correlations are taken to have the support in a
relative -invariant subregion of the full spacelike region. The
expressions for the energy density and pressure are obtained and shown to have
the same forms (in terms of an invariant distance parameter) as those of the
nonrelativistic theory and to provide the correct nonrelativistic limit
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