94 research outputs found
Transport Properties of the Diluted Lorentz Slab
We study the behavior of a point particle incident from the left on a slab of
a randomly diluted triangular array of circular scatterers. Various scattering
properties, such as the reflection and transmission probabilities and the
scattering time are studied as a function of thickness and dilution. We show
that a diffusion model satisfactorily describes the mentioned scattering
properties. We also show how some of these quantities can be evaluated exactly
and their agreement with numerical experiments. Our results exhibit the
dependence of these scattering data on the mean free path. This dependence
again shows excellent agreement with the predictions of a Brownian motion
model.Comment: 14 pages of text in LaTeX, 7 figures in Postscrip
A real Lorentz-FitzGerald contraction
Many condensed matter systems are such that their collective excitations at
low energies can be described by fields satisfying equations of motion formally
indistinguishable from those of relativistic field theory. The finite speed of
propagation of the disturbances in the effective fields (in the simplest
models, the speed of sound) plays here the role of the speed of light in
fundamental physics. However, these apparently relativistic fields are immersed
in an external Newtonian world (the condensed matter system itself and the
laboratory can be considered Newtonian, since all the velocities involved are
much smaller than the velocity of light) which provides a privileged coordinate
system and therefore seems to destroy the possibility of having a perfectly
defined relativistic emergent world. In this essay we ask ourselves the
following question: In a homogeneous condensed matter medium, is there a way
for internal observers, dealing exclusively with the low-energy collective
phenomena, to detect their state of uniform motion with respect to the medium?
By proposing a thought experiment based on the construction of a
Michelson-Morley interferometer made of quasi-particles, we show that a real
Lorentz-FitzGerald contraction takes place, so that internal observers are
unable to find out anything about their `absolute ' state of motion. Therefore,
we also show that an effective but perfectly defined relativistic world can
emerge in a fishbowl world situated inside a Newtonian (laboratory) system.
This leads us to reflect on the various levels of description in physics, in
particular regarding the quest towards a theory of quantum gravity.Comment: 6 pages, no figures. Minor changes reflect published versio
Recurrence and higher ergodic properties for quenched random Lorentz tubes in dimension bigger than two
We consider the billiard dynamics in a non-compact set of R^d that is
constructed as a bi-infinite chain of translated copies of the same
d-dimensional polytope. A random configuration of semi-dispersing scatterers is
placed in each copy. The ensemble of dynamical systems thus defined, one for
each global realization of the scatterers, is called `quenched random Lorentz
tube'. Under some fairly general conditions, we prove that every system in the
ensemble is hyperbolic and almost every system is recurrent, ergodic, and
enjoys some higher chaotic properties.Comment: Final version for J. Stat. Phys., 18 pages, 4 figure
Mach-Zehnder fiber interferometer test of the anisotropy of the speed of light
Two optical fiber Mach-Zehnder interferometers were constructed in an
environment with a temperature stabilization of better than 1 mK per day. One
interferometer with a length of 12 m optical fiber in each arm with the main
direction of the arms perpendicular to each other. Another with a length of 2 m
optical fiber in each arm where the main direction of the arms are parallel as
a control. In each arm 1 m of fiber was wound around a ring made of piezo
material enabling the control of the length of the arms by means of a voltage.
The influence of the temperature on the optical phase difference between the
interferometer arms was measured. It is attributed to the temperature change
induced variation of the interaction region of the optical fiber couplers.
Further, the influence of rotation of the interferometers at the Earth surface
on the observed phase differences was determined. For one interferometer (with
the long and perpendicular arms) it was found that the phase difference depends
on the azimuth of the interferometer. For the other one (with the short and
parallel arms) no relevant dependence on the azimuth has been measured.Comment: Errata: data of interferometers were interchange
Electrodynamics with radiation reaction
The self force of electrodynamics is derived from a scalar field. The
resulting equation of motion is free of all of the problems that plague the
Lorentz Abraham Dirac equation. The age-old problem of a particle in a constant
field is solved and the solution has intuitive appeal.Comment: 5 page
Anomalous Diffusion in Infinite Horizon Billiards
We consider the long time dependence for the moments of displacement < |r|^q
> of infinite horizon billiards, given a bounded initial distribution of
particles. For a variety of billiard models we find ~ t^g(q) (up to
factors of log t). The time exponent, g(q), is piecewise linear and equal to
q/2 for q2. We discuss the lack of dependence of this result
on the initial distribution of particles and resolve apparent discrepancies
between this time dependence and a prior result. The lack of dependence on
initial distribution follows from a remarkable scaling result that we obtain
for the time evolution of the distribution function of the angle of a
particle's velocity vector.Comment: 11 pages, 7 figures Submitted to Physical Review
Gravitation, electromagnetism and cosmological constant in purely affine gravity
The Ferraris-Kijowski purely affine Lagrangian for the electromagnetic field,
that has the form of the Maxwell Lagrangian with the metric tensor replaced by
the symmetrized Ricci tensor, is dynamically equivalent to the metric
Einstein-Maxwell Lagrangian, except the zero-field limit, for which the metric
tensor is not well-defined. This feature indicates that, for the
Ferraris-Kijowski model to be physical, there must exist a background field
that depends on the Ricci tensor. The simplest possibility, supported by recent
astronomical observations, is the cosmological constant, generated in the
purely affine formulation of gravity by the Eddington Lagrangian. In this paper
we combine the electromagnetic field and the cosmological constant in the
purely affine formulation. We show that the sum of the two affine (Eddington
and Ferraris-Kijowski) Lagrangians is dynamically inequivalent to the sum of
the analogous (CDM and Einstein-Maxwell) Lagrangians in the
metric-affine/metric formulation. We also show that such a construction is
valid, like the affine Einstein-Born-Infeld formulation, only for weak
electromagnetic fields, on the order of the magnetic field in outer space of
the Solar System. Therefore the purely affine formulation that combines
gravity, electromagnetism and cosmological constant cannot be a simple sum of
affine terms corresponding separately to these fields. A quite complicated form
of the affine equivalent of the metric Einstein-Maxwell- Lagrangian
suggests that Nature can be described by a simpler affine Lagrangian, leading
to modifications of the Einstein-Maxwell-CDM theory for
electromagnetic fields that contribute to the spacetime curvature on the same
order as the cosmological constant.Comment: 17 pages, extended and combined with gr-qc/0612193; published versio
Maxwell equations in matrix form, squaring procedure, separating the variables, and structure of electromagnetic solutions
The Riemann -- Silberstein -- Majorana -- Oppenheimer approach to the Maxwell
electrodynamics in vacuum is investigated within the matrix formalism. The
matrix form of electrodynamics includes three real 4 \times 4 matrices. Within
the squaring procedure we construct four formal solutions of the Maxwell
equations on the base of scalar Klein -- Fock -- Gordon solutions. The problem
of separating physical electromagnetic waves in the linear space
\lambda_{0}\Psi^{0}+\lambda_{1}\Psi^{1}+\lambda_{2}\Psi^{2}+ lambda_{3}\Psi^{3}
is investigated, several particular cases, plane waves and cylindrical waves,
are considered in detail.Comment: 26 pages 16 International Seminar NCPC, May 19-22, 2009, Minsk,
Belaru
Chaotic Inflationary Universe on Brane
The chaotic inflationary model of the early universe, proposed by Linde is
explored in the brane world considering matter described by a minimally coupled
self interacting scalar field. We obtain cosmological solutions which admit
evolution of a universe either from a singularity or without a singularity. It
is found that a very weakly coupled self-interacting scalar field is necessary
for a quartic type potential in the brane world model compared to that
necessary in general relativity. In the brane world sufficient inflation may be
obtained even with an initial scalar field having value less than the Planck
scale. It is found that if the universe is kinetic energy dominated to begin
with, it transits to an inflationary stage subsequently.Comment: 13 pages, no fig., accepted in Physical Review
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