661 research outputs found
Gaussian fields and Gaussian sheets with generalized Cauchy covariance structure
Two types of Gaussian processes, namely the Gaussian field with generalized
Cauchy covariance (GFGCC) and the Gaussian sheet with generalized Cauchy
covariance (GSGCC) are considered. Some of the basic properties and the
asymptotic properties of the spectral densities of these random fields are
studied. The associated self-similar random fields obtained by applying the
Lamperti transformation to GFGCC and GSGCC are studied.Comment: 32 pages, 6 figure
Modeling Single-File Diffusion by Step Fractional Brownian Motion and Generalized Fractional Langevin Equation
Single-file diffusion behaves as normal diffusion at small time and as
anomalous subdiffusion at large time. These properties can be described by
fractional Brownian motion with variable Hurst exponent or multifractional
Brownian motion. We introduce a new stochastic process called Riemann-Liouville
step fractional Brownian motion which can be regarded as a special case of
multifractional Brownian motion with step function type of Hurst exponent
tailored for single-file diffusion. Such a step fractional Brownian motion can
be obtained as solution of fractional Langevin equation with zero damping.
Various types of fractional Langevin equations and their generalizations are
then considered to decide whether their solutions provide the correct
description of the long and short time behaviors of single-file diffusion. The
cases where dissipative memory kernel is a Dirac delta function, a power-law
function, and a combination of both of these functions, are studied in detail.
In addition to the case where the short time behavior of single-file diffusion
behaves as normal diffusion, we also consider the possibility of the process
that begins as ballistic motion.Comment: 12 pages, 7 figure
Finite Temperature Casimir Effect and Dispersion in the Presence of Compactified Extra Dimensions
Finite temperature Casimir theory of the Dirichlet scalar field is developed,
assuming that there is a conventional Casimir setup in physical space with two
infinitely large plates separated by a gap R and in addition an arbitrary
number q of extra compacified dimensions. As a generalization of earlier
theory, we assume in the first part of the paper that there is a scalar
'refractive index' N filling the whole of the physical space region. After
presenting general expressions for free energy and Casimir forces we focus on
the low temperature case, as this is of main physical interest both for force
measurements and also for issues related to entropy and the Nernst theorem.
Thereafter, in the second part we analyze dispersive properties, assuming for
simplicity q=1, by taking into account dispersion associated with the first
Matsubara frequency only. The medium-induced contribution to the free energy,
and pressure, is calculated at low temperatures.Comment: 25 pages, one figure. Minor changes in the discussion. Version to
appear in Physica Script
Finite temperature Casimir pistons for electromagnetic field with mixed boundary conditions and its classical limit
In this paper, the finite temperature Casimir force acting on a
two-dimensional Casimir piston due to electromagnetic field is computed. It was
found that if mixed boundary conditions are assumed on the piston and its
opposite wall, then the Casimir force always tends to restore the piston
towards the equilibrium position, regardless of the boundary conditions assumed
on the walls transverse to the piston. In contrary, if pure boundary conditions
are assumed on the piston and the opposite wall, then the Casimir force always
tend to pull the piston towards the closer wall and away from the equilibrium
position. The nature of the force is not affected by temperature. However, in
the high temperature regime, the magnitude of the Casimir force grows linearly
with respect to temperature. This shows that the Casimir effect has a classical
limit as has been observed in other literatures.Comment: 14 pages, 3 figures, accepted by Journal of Physics
Finite Temperature Casimir Effect in Randall-Sundrum Models
The finite temperature Casimir effect for a scalar field in the bulk region
of the two Randall-Sundrum models, RSI and RSII, is studied. We calculate the
Casimir energy and the Casimir force for two parallel plates with separation
on the visible brane in the RSI model. High-temperature and low-temperature
cases are covered. Attractiveness versus repulsiveness of the temperature
correction to the force is discussed in the typical special cases of
Dirichlet-Dirichlet, Neumann-Neumann, and Dirichlet-Neumann boundary conditions
at low temperature. The Abel-Plana summation formula is made use of, as this
turns out to be most convenient. Some comments are made on the related
contemporary literature.Comment: 33 pages latex, 2 figures. Some changes in the discussion. To appear
in New J. Phy
On the minima and convexity of Epstein Zeta function
Let be the Epstein zeta function defined as the
meromorphic continuation of the function
\sum_{k\in\Z^n\setminus\{0\}}(\sum_{i=1}^n [a_i k_i]^2)^{-s},
\text{Re} s>\frac{n}{2}
to the complex plane. We show that for fixed , the function
, as a function of with
fixed , has a unique minimum at the point .
When is fixed, the function can be shown to be a convex function of any of
the variables . These results are then applied to the study of
the sign of when is in the critical range . It is shown that when , as a
function of , can be both positive and negative for
every . When , there are some open subsets of
, where is positive for all . By regarding as a function of , we
find that when , the generalized Riemann hypothesis is false for all
.Comment: 27 page
Finite Temperature Casimir Effect for a Massless Fractional Klein-Gordon field with Fractional Neumann Conditions
This paper studies the Casimir effect due to fractional massless Klein-Gordon
field confined to parallel plates. A new kind of boundary condition called
fractional Neumann condition which involves vanishing fractional derivatives of
the field is introduced. The fractional Neumann condition allows the
interpolation of Dirichlet and Neumann conditions imposed on the two plates.
There exists a transition value in the difference between the orders of the
fractional Neumann conditions for which the Casimir force changes from
attractive to repulsive. Low and high temperature limits of Casimir energy and
pressure are obtained. For sufficiently high temperature, these quantities are
dominated by terms independent of the boundary conditions. Finally, validity of
the temperature inversion symmetry for various boundary conditions is
discussed.Comment: 31 page
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