12,163 research outputs found

### The Hausdorff moments in statistical mechanics

A new method for solving the Hausdorff moment problem is presented which makes use of Pollaczek polynomials. This problem is severely ill posed; a regularized solution is obtained without any use of prior knowledge. When the problem is treated in the L 2 space and the moments are finite in number and affected by noise or roundâoff errors, the approximation converges asymptotically in the L 2 norm. The method is applied to various questions of statistical mechanics and in particular to the determination of the density of states. Concerning this latter problem the method is extended to include distribution valued densities. Computing the Laplace transform of the expansion a new series representation of the partition function Z(ÎČ) (ÎČ=1/k BT ) is obtained which coincides with a Watson resummation of the highâtemperature series for Z(ÎČ)

### Radiating black hole solutions in Einstein-Gauss-Bonnet gravity

In this paper, we find some new exact solutions to the Einstein-Gauss-Bonnet
equations. First, we prove a theorem which allows us to find a large family of
solutions to the Einstein-Gauss-Bonnet gravity in $n$-dimensions. This family
of solutions represents dynamic black holes and contains, as particular cases,
not only the recently found Vaidya-Einstein-Gauss-Bonnet black hole, but also
other physical solutions that we think are new, such as, the Gauss-Bonnet
versions of the Bonnor-Vaidya(de Sitter/anti-de Sitter) solution, a global
monopole and the Husain black holes. We also present a more general version of
this theorem in which less restrictive conditions on the energy-momentum tensor
are imposed. As an application of this theorem, we present the exact solution
describing a black hole radiating a charged null fluid in a Born-Infeld
nonlinear electrodynamics

### Self-Interacting Electromagnetic Fields and a Classical Discussion on the Stability of the Electric Charge

The present work proposes a discussion on the self-energy of charged
particles in the framework of nonlinear electrodynamics. We seek magnet- ically
stable solutions generated by purely electric charges whose electric and
magnetic fields are computed as solutions to the Born-Infeld equa- tions. The
approach yields rich internal structures that can be described in terms of the
physical fields with explicit analytic solutions. This suggests that the
anomalous field probably originates from a magnetic excitation in the vacuum
due to the presence of the very intense electric field. In addition, the
magnetic contribution has been found to exert a negative pressure on the
charge. This, in turn, balances the electric repulsion, in such a way that the
self-interaction of the field appears as a simple and natural classical
mechanism that is able to account for the stability of the electron charge.Comment: 8 pages, 1 figur

### Reciprocal relativity of noninertial frames and the quaplectic group

Newtonian mechanics has the concept of an absolute inertial rest frame.
Special relativity eliminates the absolute rest frame but continues to require
the absolute inertial frame. General relativity solves this for gravity by
requiring particles to have locally inertial frames on a curved position-time
manifold. The problem of the absolute inertial frame for other forces remains.
We look again at the transformations of frames on an extended phase space with
position, time, energy and momentum degrees of freedom. Under nonrelativistic
assumptions, there is an invariant symplectic metric and a line element dt^2.
Under special relativistic assumptions the symplectic metric continues to be
invariant but the line elements are now -dt^2+dq^2/c^2 and dp^2-de^2/c^2. Max
Born conjectured that the line element should be generalized to the pseudo-
orthogonal metric -dt^2+dq^2/c^2+ (1/b^2)(dp^2-de^2/c^2). The group leaving
these two metrics invariant is the pseudo-unitary group of transformations
between noninertial frames. We show that these transformations eliminate the
need for an absolute inertial frame by making forces relative and bounded by b
and so embodies a relativity that is 'reciprocal' in the sense of Born. The
inhomogeneous version of this group is naturally the semidirect product of the
pseudo-unitary group with the nonabelian Heisenberg group. This is the
quaplectic group. The Heisenberg group itself is the semidirect product of two
translation groups. This provides the noncommutative properties of position and
momentum and also time and energy that are required for the quantum mechanics
that results from considering the unitary representations of the quaplectic
group.Comment: Substantial revision, Publicon LaTe

### Selfduality of non-linear electrodynamics with derivative corrections

In this paper we investigate how electromagnetic duality survives derivative
corrections to classical non-linear electrodynamics. In particular, we
establish that electromagnetic selfduality is satisfied to all orders in
$\alpha'$ for the four-point function sector of the four dimensional open
string effective action.Comment: 8 page

### Nonlinear Maxwell Equations

A new relativistic invariant version of nonlinear Maxwell equations is
offerred. Some properties of these equations are considered.Comment: 6 pages, LaTe

### Casimir effect across a layered medium

Using nonstandard recursion relations for Fresnel coefficients involving
successive stacks of layers, we extend the Lifshitz formula to configurations
with an inhomogeneous, n-layered, medium separating two planar objects. The
force on each object is the sum of a Lifshitz like force and a force arising
from the inhomogeneity of the medium. The theory correctly reproduces very
recently obtained results for the Casimir force/energy in some simple systems
of this kind. As a by product, we obtain a formula for the force on an
(unspecified) stack of layers between two planar objects which generalizes our
previous result for the force on a slab in a planar cavity.Comment: 5 pages, 1 figure, presented at QFEXT1

### Quasinormal modes, quantized black holes, and correspondence principle

Contrary to the wide-spread belief, the correspondence principle does not
dictate any relation between the asymptotics of quasinormal modes and the
spectrum of quantized black holes. Moreover, this belief is in conflict with
simple physical arguments.Comment: 2 pages; a new argument adde

### Comment on `On the Quantum Theory of Molecules' [J. Chem.Phys. {\bf 137}, 22A544 (2012)]

In our previous paper [J. Chem.Phys. {\bf 137}, 22A544 (2012)] we argued that
the Born-Oppenheimer approximation could not be based on an exact
transformation of the molecular Schr\"{o}dinger equation. In this Comment we
suggest that the fundamental reason for the approximate nature of the
Born-Oppenheimer model is the lack of a complete set of functions for the
electronic space, and the need to describe the continuous spectrum using
spectral projection.Comment: 2 page

### Cosmology with a Nonlinear Born-Infeld type Scalar Field

Recent many physicists suggest that the dark energy in the universe might
result from the Born-Infeld(B-I) type scalar field of string theory. The
universe of B-I type scalar field with potential can undergo a phase of
accelerating expansion. The corresponding equation of state parameter lies in
the range of $\displaystyle -1<\omega<-{1/3}$. The equation of state parameter
of B-I type scalar field without potential lies in the range of
$0\leq\omega\leq1$. We find that weak energy condition and strong energy
condition are violated for phantom B-I type scalar field. The equation of state
parameter lies in the range of $\omega<-1$.Comment: 10 pages without figure

- âŠ