886 research outputs found
Mixing of the symmetric exclusion processes in terms of the corresponding single-particle random walk
We prove an upper bound for the -mixing time of the symmetric
exclusion process on any graph G, with any feasible number of particles. Our
estimate is proportional to ,
where |V| is the number of vertices in G, and is
the 1/4-mixing time of the corresponding single-particle random walk. This
bound implies new results for symmetric exclusion on expanders, percolation
clusters, the giant component of the Erdos-Renyi random graph and Poisson point
processes in . Our technical tools include a variant of Morris's
chameleon process.Comment: Published in at http://dx.doi.org/10.1214/11-AOP714 the Annals of
Probability (http://www.imstat.org/aop/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Spectral Zeta Functions for a Cylinder and a Circle
Spectral zeta functions for the massless scalar fields obeying the
Dirichlet and Neumann boundary conditions on a surface of an infinite cylinder
are constructed. These functions are defined explicitly in a finite domain of
the complex plane s containing the closed interval of real axis Re . Proceeding from this the spectral zeta functions for the boundary
conditions given on a circle (boundary value problem on a plane) are obtained
without any additional calculations. The Casimir energy for the relevant field
configurations is deduced.Comment: REVTeX4, 13 pages, no tables and figures; v2 some misprints are
correcte
New analytic running coupling in QCD: higher loop levels
The properties of the new analytic running coupling are investigated at the
higher loop levels. The expression for this invariant charge, independent of
the normalization point, is obtained by invoking the asymptotic freedom
condition. It is shown that at any loop level the relevant function has
the universal behaviors at small and large values of the invariant charge. Due
to this feature the new analytic running coupling possesses the universal
asymptotics both in the ultraviolet and infrared regions irrespective of the
loop level. The consistency of the model considered with the general definition
of the QCD invariant charge is shown.Comment: LaTeX 2.09, 12 pages with 5 EPS figures, uses mpla1.sty; enlarged
version is accepted for publication in Mod. Phys. Lett.
Casimir energy of a non-uniform string
The Casimir energy of a non-uniform string built up from two pieces with
different speed of sound is calculated. A standard procedure of subtracting the
energy of an infinite uniform string is applied, the subtraction being
interpreted as the renormalization of the string tension. It is shown that in
the case of a homogeneous string this method is completely equivalent to the
zeta renormalization.Comment: 11 pages, REVTeX, no figures and table
Analytic invariant charge and the lattice static quark-antiquark potential
A recently developed model for the QCD analytic invariant charge is compared
with quenched lattice simulation data on the static quark-antiquark potential.
By employing this strong running coupling one is able to obtain the confining
quark-antiquark potential in the framework of the one-gluon exchange model. To
achieve this objective a technique for evaluating the integrals of a required
form is developed. Special attention is paid here to removing the divergences
encountered the calculations. All this enables one to examine the asymptotic
behavior of the potential at both small and large distances with high accuracy.
An explicit expression for the quark-antiquark potential, which interpolates
between these asymptotics, and satisfies the concavity condition, is proposed.
The derived potential coincides with the perturbative results at small
distances, and it is in a good agreement with the lattice data in the
nonperturbative physically-relevant region. An estimation of the parameter
is obtained for the case of pure gluodynamics. It is found to
be consistent with all the previous estimations of in the
framework of approach in hand.Comment: LaTeX2e, 10 pages with 3 EPS figure
A thick shell Casimir effect
We consider the Casimir energy of a thick dielectric-diamagnetic shell under
a uniform velocity light condition, as a function of the radii and the
permeabilities. We show that there is a range of parameters in which the stress
on the outer shell is inward, and a range where the stress on the outer shell
is outward. We examine the possibility of obtaining an energetically stable
configuration of a thick shell made of a material with a fixed volume
Casimir energy of a dilute dielectric ball in the mode summation method
In the --approximation the Casimir energy of a
dilute dielectric ball is derived using a simple and clear method of the mode
summation. The addition theorem for the Bessel functions enables one to present
in a closed form the sum over the angular momentum before the integration over
the imaginary frequencies. The linear in contribution
into the vacuum energy is removed by an appropriate subtraction. The role of
the contact terms used in other approaches to this problem is elucidated.Comment: 14 pages, REVTeX, no figures, no tables; presentation is made better,
new references are adde
- …