7,507 research outputs found
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 -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
Coupled dynamics of atoms and radiation pressure driven interferometers
We consider the motion of the end mirror of a cavity in whose standing wave
mode pattern atoms are trapped. The atoms and the light field strongly couple
to each other because the atoms form a distributed Bragg mirror with a
reflectivity that can be fairly high. We analyze how the dipole potential in
which the atoms move is modified due to this backaction of the atoms. We show
that the position of the atoms can become bistable. These results are of a more
general nature and can be applied to any situation where atoms are trapped in
an optical lattice inside a cavity and where the backaction of the atoms on the
light field cannot be neglected. We analyze the dynamics of the coupled system
in the adiabatic limit where the light field adjusts to the position of the
atoms and the light field instantaneously and where the atoms move much faster
than the mirror. We calculate the side band spectrum of the light transmitted
through the cavity and show that these spectra can be used to detect the
coupled motion of the atoms and the mirror.Comment: 11 pages; 13 figures; two added references and other minor
correction
(Never) Mind your p's and q's: Von Neumann versus Jordan on the Foundations of Quantum Theory
In two papers entitled "On a new foundation [Neue Begr\"undung] of quantum
mechanics," Pascual Jordan (1927b,g) presented his version of what came to be
known as the Dirac-Jordan statistical transformation theory. As an alternative
that avoids the mathematical difficulties facing the approach of Jordan and
Paul A. M. Dirac (1927), John von Neumann (1927a) developed the modern Hilbert
space formalism of quantum mechanics. In this paper, we focus on Jordan and von
Neumann. Central to the formalisms of both are expressions for conditional
probabilities of finding some value for one quantity given the value of
another. Beyond that Jordan and von Neumann had very different views about the
appropriate formulation of problems in quantum mechanics. For Jordan, unable to
let go of the analogy to classical mechanics, the solution of such problems
required the identication of sets of canonically conjugate variables, i.e., p's
and q's. For von Neumann, not constrained by the analogy to classical
mechanics, it required only the identication of a maximal set of commuting
operators with simultaneous eigenstates. He had no need for p's and q's. Jordan
and von Neumann also stated the characteristic new rules for probabilities in
quantum mechanics somewhat differently. Jordan (1927b) was the first to state
those rules in full generality. Von Neumann (1927a) rephrased them and, in a
subsequent paper (von Neumann, 1927b), sought to derive them from more basic
considerations. In this paper we reconstruct the central arguments of these
1927 papers by Jordan and von Neumann and of a paper on Jordan's approach by
Hilbert, von Neumann, and Nordheim (1928). We highlight those elements in these
papers that bring out the gradual loosening of the ties between the new quantum
formalism and classical mechanics.Comment: New version. The main difference with the old version is that the
introduction has been rewritten. Sec. 1 (pp. 2-12) in the old version has
been replaced by Secs. 1.1-1.4 (pp. 2-31) in the new version. The paper has
been accepted for publication in European Physical Journal
Nonperturbative calculation of Born-Infeld effects on the Schroedinger spectrum of the hydrogen atom
We present the first nonperturbative numerical calculations of the
nonrelativistic hydrogen spectrum as predicted by first-quantized
electrodynamics with nonlinear Maxwell-Born-Infeld field equations. We also
show rigorous upper and lower bounds on the ground state.
When judged against empirical data our results significantly restrict the
range of viable values of the new electromagnetic constant which is introduced
by the Born-Infeld theory.
We assess Born's own proposal for the value of his constant.Comment: 4p., 2 figs, 1 table; submitted for publicatio
Singularity-Free Electrodynamics for Point Charges and Dipoles: Classical Model for Electron Self-Energy and Spin
It is shown how point charges and point dipoles with finite self-energies can
be accomodated into classical electrodynamics. The key idea is the introduction
of constitutive relations for the electromagnetic vacuum, which actually
mirrors the physical reality of vacuum polarization. Our results reduce to
conventional electrodynamics for scales large compared to the classical
electron radius cm. A classical simulation for a
structureless electron is proposed, with the appropriate values of mass, spin
and magnetic moment.Comment: 3 page
Dynamics of the Born-Infeld dyons
The approach to the dynamics of a charged particle in the Born-Infeld
nonlinear electrodynamics developed in [Phys. Lett. A 240 (1998) 8] is
generalized to include a Born-Infeld dyon. Both Hamiltonian and Lagrangian
structures of many dyons interacting with nonlinear electromagnetism are
constructed. All results are manifestly duality invariant.Comment: 11 pages, LATE
On the physical origins of the negative index of refraction
The physical origins of negative refractive index are derived from a dilute
microscopic model, producing a result that is generalized to the dense
condensed phase limit. In particular, scattering from a thin sheet of electric
and magnetic dipoles driven above resonance is used to form a fundamental
description for negative refraction. Of practical significance, loss and
dispersion are implicit in the microscopic model. While naturally occurring
negative index materials are unavailable, ferromagnetic and ferroelectric
materials provide device design opportunities.Comment: 4 pages, 1 figur
An electronic Mach-Zehnder interferometer in the Fractional Quantum Hall effect
We compute the interference pattern of a Mach-Zehnder interferometer
operating in the fractional quantum Hall effect. Our theoretical proposal is
inspired by a remarkable experiment on edge states in the Integer Quantum Hall
effect (IQHE). The Luttinger liquid model is solved via two independent
methods: refermionization at nu=1/2 and the Bethe Ansatz solution available for
Laughlin fractions. The current differs strongly from that of single electrons
in the strong backscattering regime. The Fano factor is periodic in the flux,
and it exhibits a sharp transition from sub-Poissonian (charge e/2) to
Poissonian (charge e) in the neighborhood of destructive interferences
Transformation Optics with Photonic Band Gap Media
We introduce a class of optical media based on adiabatically modulated,
dielectric-only, and potentially extremely low-loss, photonic crystals. The
media we describe represent a generalization of the eikonal limit of
transformation optics (TO). The foundation of the concept is the possibility to
fit frequency isosurfaces in the k-space of photonic crystals with elliptic
surfaces, allowing them to mimic the dispersion relation of light in
anisotropic effective media. Photonic crystal cloaks and other TO devices
operating at visible wavelengths can be constructed from optically transparent
substances like glasses, whose attenuation coefficient can be as small as 10
dB/km, suggesting the TO design methodology can be applied to the development
of optical devices not limited by the losses inherent to metal-based, passive
metamaterials.Comment: 4 pages, 4 figure
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