801 research outputs found
The Three Loop Equation of State of QED at High Temperature
We present the three loop contribution (order ) to the pressure of
massless quantum electrodynamics at nonzero temperature. The calculation is
performed within the imaginary time formalism. Dimensional regularization is
used to handle the usual, intermediate stage, ultraviolet and infrared
singularities, and also to prevent overcounting of diagrams during resummation.Comment: ANL-HEP-PR-94-02, SPhT/94-054 (revised final version
Solution to the 3-loop -derivable Approximation for Scalar Thermodynamics
We solve the 3-loop -derivable approximation to the thermodynamics of
the massless field theory by reducing it to a 1-parameter variational
problem. The thermodynamic potential is expanded in powers of and ,
where is the coupling constant, is a variational mass parameter, and
is the temperature. There are ultraviolet divergences beginning at 6th
order in that cannot be removed by renormalization. However the finite
thermodynamic potential obtained by truncating after terms of 5th order in
and defines a stable approximation to the thermodynamic functions.Comment: 4 pages, 1 figur
The Equation of State for Dense QCD and Quark Stars
We calculate the equation of state for degenerate quark matter to leading
order in hard-dense-loop (HDL) perturbation theory. We solve the
Tolman-Oppenheimer-Volkov equations to obtain the mass-radius relation for
dense quark stars. Both the perturbative QCD and the HDL equations of state
have a large variation with respect to the renormalization scale for quark
chemical potential below 1 GeV which leads to large theoretical uncertainties
in the quark star mass-radius relation.Comment: 7 pages, 3 figure
Quark number susceptibilities of hot QCD up to g^6ln(g)
The pressure of hot QCD has recently been determined to the last
perturbatively computable order g^6 ln(g) by Kajantie et al. using
three-dimensional effective theories. A similar method is applied here to the
pressure in the presence of small but non-vanishing quark chemical potentials,
and the result is used to derive the quark number susceptibilities in the limit
mu = 0. The diagonal quark number susceptibility of QCD with n_f flavours of
massless quarks is evaluated to order g^6ln(g) and compared with recent lattice
simulations. It is observed that the results qualitatively resemble the lattice
ones, and that when combined with the fully perturbative but yet undetermined
g^6 term they may well explain the behaviour of the lattice data for a wide
range of temperatures.Comment: 11 pages, 3 figures Typos corrected, references added, figures
modifie
The Non-Trapping Degree of Scattering
We consider classical potential scattering. If no orbit is trapped at energy
E, the Hamiltonian dynamics defines an integer-valued topological degree. This
can be calculated explicitly and be used for symbolic dynamics of
multi-obstacle scattering.
If the potential is bounded, then in the non-trapping case the boundary of
Hill's Region is empty or homeomorphic to a sphere.
We consider classical potential scattering. If at energy E no orbit is
trapped, the Hamiltonian dynamics defines an integer-valued topological degree
deg(E) < 2. This is calculated explicitly for all potentials, and exactly the
integers < 2 are shown to occur for suitable potentials.
The non-trapping condition is restrictive in the sense that for a bounded
potential it is shown to imply that the boundary of Hill's Region in
configuration space is either empty or homeomorphic to a sphere.
However, in many situations one can decompose a potential into a sum of
non-trapping potentials with non-trivial degree and embed symbolic dynamics of
multi-obstacle scattering. This comprises a large number of earlier results,
obtained by different authors on multi-obstacle scattering.Comment: 25 pages, 1 figure Revised and enlarged version, containing more
detailed proofs and remark
On the screening of static electromagnetic fields in hot QED plasmas
We study the screening of static magnetic and electric fields in massless
quantum electrodynamics (QED) and massless scalar electrodynamics (SQED) at
temperature . Various exact relations for the static polarisation tensor are
first reviewed and then verified perturbatively to fifth order (in the
coupling) in QED and fourth order in SQED, using different resummation
techniques. The magnetic and electric screening masses squared, as defined
through the pole of the static propagators, are also calculated to fifth order
in QED and fourth order in SQED, and their gauge-independence and
renormalisation-group invariance is checked. Finally, we provide arguments for
the vanishing of the magnetic mass to all orders in perturbation theory.Comment: 37 pages, 8 figure
Population dynamical behavior of Lotka-Volterra system under regime switching
In this paper, we investigate a Lotka-Volterra system under regime switching dx(t) = diag(x1(t); : : : ; xn(t))[(b(r(t)) + A(r(t))x(t))dt + (r(t))dB(t)]; where B(t) is a standard Brownian motion. The aim here is to find out what happens under regime switching. We first obtain the sufficient conditions for the existence of global positive solutions, stochastic permanence and extinction. We find out that both stochastic permanence and extinction have close relationships with the stationary probability distribution of the Markov chain. The limit of the average in time of the sample path of the solution is then estimated by two constants related to the stationary distribution and the coefficients. Finally, the main results are illustrated by several examples
Small, Dense Quark Stars from Perturbative QCD
As a model for nonideal behavior in the equation of state of QCD at high
density, we consider cold quark matter in perturbation theory. To second order
in the strong coupling constant, , the results depend sensitively on
the choice of the renormalization mass scale. Certain choices of this scale
correspond to a strongly first order chiral transition, and generate quark
stars with maximum masses and radii approximately half that of ordinary neutron
stars. At the center of these stars, quarks are essentially massless.Comment: ReVTeX, 5 pages, 3 figure
One Loop Renormalization of the Littlest Higgs Model
In Little Higgs models a collective symmetry prevents the Higgs from
acquiring a quadratically divergent mass at one loop. This collective symmetry
is broken by weakly gauged interactions. Terms, like Yukawa couplings, that
display collective symmetry in the bare Lagrangian are generically renormalized
into a sum of terms that do not respect the collective symmetry except possibly
at one renormalization point where the couplings are related so that the
symmetry is restored. We study here the one loop renormalization of a
prototypical example, the Littlest Higgs Model. Some features of the
renormalization of this model are novel, unfamiliar form similar chiral
Lagrangian studies.Comment: 23 pages, 17 eps figure
Approximately self-consistent resummations for the thermodynamics of the quark-gluon plasma. I. Entropy and density
We propose a gauge-invariant and manifestly UV finite resummation of the
physics of hard thermal/dense loops (HTL/HDL) in the thermodynamics of the
quark-gluon plasma. The starting point is a simple, effectively one-loop
expression for the entropy or the quark density which is derived from the fully
self-consistent two-loop skeleton approximation to the free energy, but subject
to further approximations, whose quality is tested in a scalar toy model. In
contrast to the direct HTL/HDL-resummation of the one-loop free energy, in our
approach both the leading-order (LO) and the next-to-leading order (NLO)
effects of interactions are correctly reproduced and arise from kinematical
regimes where the HTL/HDL are justifiable approximations. The LO effects are
entirely due to the (asymptotic) thermal masses of the hard particles. The NLO
ones receive contributions both from soft excitations, as described by the
HTL/HDL propagators, and from corrections to the dispersion relation of the
hard excitations, as given by HTL/HDL perturbation theory. The numerical
evaluations of our final expressions show very good agreement with lattice data
for zero-density QCD, for temperatures above twice the transition temperature.Comment: 62 pages REVTEX, 14 figures; v2: numerous clarifications, sect. 2C
shortened, new material in sect. 3C; v3: more clarifications, one appendix
removed, alternative implementation of the NLO effects, corrected eq. (5.16
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