794 research outputs found
On some geometric features of the Kramer interior solution for a rotating perfect fluid
Geometric features (including convexity properties) of an exact interior
gravitational field due to a self-gravitating axisymmetric body of perfect
fluid in stationary, rigid rotation are studied. In spite of the seemingly
non-Newtonian features of the bounding surface for some rotation rates, we
show, by means of a detailed analysis of the three-dimensional spatial
geodesics, that the standard Newtonian convexity properties do hold. A central
role is played by a family of geodesics that are introduced here, and provide a
generalization of the Newtonian straight lines parallel to the axis of
rotation.Comment: LaTeX, 15 pages with 4 Poscript figures. To be published in Classical
and Quantum Gravit
On the ill-posed character of the Lorentz integral transform
An exact inversion formula for the Lorentz integral transform (LIT) is
provided together with the spectrum of the LIT kernel. The exponential increase
of the inverse Fourier transform of the LIT kernel entering the inversion
formula explains the ill-posed character of the LIT approach. Also the
continuous spectrum of the LIT kernel, which approaches zero points necessarily
to the same defect. A possible cure is discussed and numerically illustrated.Comment: 13 pages, 3 figure
Sommerfeld's image method in the calculation of van der Waals forces
We show how the image method can be used together with a recent method
developed by C. Eberlein and R. Zietal to obtain the dispersive van der Waals
interaction between an atom and a perfectly conducting surface of arbitrary
shape. We discuss in detail the case of an atom and a semi- infinite conducting
plane. In order to employ the above procedure to this problem it is necessary
to use the ingenious image method introduced by Sommerfeld more than one
century ago, which is a generalization of the standard procedure. Finally, we
briefly discuss other interesting situations that can also be treated by the
joint use of Sommerfeld's image technique and Eberlein-Zietal method.Comment: To appear in the proceedings of Conference on Quantum Field Theory
under the Influence of External Conditions (QFEXT11
Transport in Transitory, Three-Dimensional, Liouville Flows
We derive an action-flux formula to compute the volumes of lobes quantifying
transport between past- and future-invariant Lagrangian coherent structures of
n-dimensional, transitory, globally Liouville flows. A transitory system is one
that is nonautonomous only on a compact time interval. This method requires
relatively little Lagrangian information about the codimension-one surfaces
bounding the lobes, relying only on the generalized actions of loops on the
lobe boundaries. These are easily computed since the vector fields are
autonomous before and after the time-dependent transition. Two examples in
three-dimensions are studied: a transitory ABC flow and a model of a
microdroplet moving through a microfluidic channel mixer. In both cases the
action-flux computations of transport are compared to those obtained using
Monte Carlo methods.Comment: 30 pages, 16 figures, 1 table, submitted to SIAM J. Appl. Dyn. Sy
Regularization of static self-forces
Various regularization methods have been used to compute the self-force
acting on a static particle in a static, curved spacetime. Many of these are
based on Hadamard's two-point function in three dimensions. On the other hand,
the regularization method that enjoys the best justification is that of
Detweiler and Whiting, which is based on a four-dimensional Green's function.
We establish the connection between these methods and find that they are all
equivalent, in the sense that they all lead to the same static self-force. For
general static spacetimes, we compute local expansions of the Green's functions
on which the various regularization methods are based. We find that these agree
up to a certain high order, and conjecture that they might be equal to all
orders. We show that this equivalence is exact in the case of ultrastatic
spacetimes. Finally, our computations are exploited to provide regularization
parameters for a static particle in a general static and spherically-symmetric
spacetime.Comment: 23 pages, no figure
Mutually unbiased bases in dimension six: The four most distant bases
We consider the average distance between four bases in dimension six. The
distance between two orthonormal bases vanishes when the bases are the same,
and the distance reaches its maximal value of unity when the bases are
unbiased. We perform a numerical search for the maximum average distance and
find it to be strictly smaller than unity. This is strong evidence that no four
mutually unbiased bases exist in dimension six. We also provide a two-parameter
family of three bases which, together with the canonical basis, reach the
numerically-found maximum of the average distance, and we conduct a detailed
study of the structure of the extremal set of bases.Comment: 10 pages, 2 figures, 1 tabl
Unbiased bases (Hadamards) for 6-level systems: Four ways from Fourier
In quantum mechanics some properties are maximally incompatible, such as the
position and momentum of a particle or the vertical and horizontal projections
of a 2-level spin. Given any definite state of one property the other property
is completely random, or unbiased. For N-level systems, the 6-level ones are
the smallest for which a tomographically efficient set of N+1 mutually unbiased
bases (MUBs) has not been found. To facilitate the search, we numerically
extend the classification of unbiased bases, or Hadamards, by incrementally
adjusting relative phases in a standard basis. We consider the non-unitarity
caused by small adjustments with a second order Taylor expansion, and choose
incremental steps within the 4-dimensional nullspace of the curvature. In this
way we prescribe a numerical integration of a 4-parameter set of Hadamards of
order 6.Comment: 5 pages, 2 figure
Estimates on Green functions of second order differential operators with singular coefficients
We investigate the Green functions G(x,x^{\prime}) of some second order
differential operators on R^{d+1} with singular coefficients depending only on
one coordinate x_{0}. We express the Green functions by means of the Brownian
motion. Applying probabilistic methods we prove that when x=(0,{\bf x}) and
x^{\prime}=(0,{\bf x}^{\prime}) (here x_{0}=0) lie on the singular hyperplanes
then G(0,{\bf x};0,{\bf x}^{\prime}) is more regular than the Green function of
operators with regular coefficients.Comment: 16 page
A nongravitational wormhole
Using the effective metric formalism for photons in a nonlinear
electromagnetic theory, we show that a certain field configuration in
Born-Infeld electromagnetism in flat spacetime can be interpreted as an
ultrastatic spherically symmetric wormhole. We also discuss some properties of
the effective metric that are valid for any field configuration.Comment: LaTex, 9 pages with 5 figures, minor changes, accepted for
publication in Class. Quantum Gra
Birefringence in nonlinear anisotropic dielectric media
Light propagation is investigated in the context of local anisotropic
nonlinear dielectric media at rest with the dielectric coefficients
and constant ,
in the limit of geometrical optics. Birefringence was examined and the general
conditions for its occurrence were presented. A toy model is exhibited, in
which uniaxial birefringent media with nonlinear dielectric properties could be
driven by external fields in such way that birefringence may be artificially
controlled. The effective geometry interpretation is also addressed.Comment: 5 pages, 1 figur
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