1,603 research outputs found
Deterministic Walks in Quenched Random Environments of Chaotic Maps
This paper concerns the propagation of particles through a quenched random
medium. In the one- and two-dimensional models considered, the local dynamics
is given by expanding circle maps and hyperbolic toral automorphisms,
respectively. The particle motion in both models is chaotic and found to
fluctuate about a linear drift. In the proper scaling limit, the cumulative
distribution function of the fluctuations converges to a Gaussian one with
system dependent variance while the density function shows no convergence to
any function. We have verified our analytical results using extreme precision
numerical computations.Comment: 18 pages, 9 figure
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
The Averaging Problem in Cosmology and Macroscopic Gravity
The averaging problem in cosmology and the approach of macroscopic gravity to
resolve the problem is discussed. The averaged Einstein equations of
macroscopic gravity are modified on cosmological scales by the macroscopic
gravitational correlation tensor terms as compared with the Einstein equations
of general relativity. This correlation tensor satisfies a system of structure
and field equations. An exact cosmological solution to the macroscopic gravity
equations for a constant macroscopic gravitational connection correlation
tensor for a flat spatially homogeneous, isotropic macroscopic space-time is
presented. The correlation tensor term in the macroscopic Einstein equations
has been found to take the form of either a negative or positive spatial
curvature term. Thus, macroscopic gravity provides a cosmological model for a
flat spatially homogeneous, isotropic Universe which obeys the dynamical law
for either an open or closed Universe.Comment: 8 pages, LaTeX, ws-ijmpa.cls, few style and typo corrections. Based
on the plenary talk given at the Second Stueckelberg Workshop, ICRANet
Coordinating Center, Pescara, Italy, September 3-7, 2007. To appear in
International Journal of Modern Physics A (2008
Observation of light dragging in rubidium vapor cell
We report on the experimental demonstration of light dragging effect due to
atomic motion in a rubidium vapor cell. We found that the minimum group
velocity is achieved for light red-shifted from the center of the atomic
resonance, and that the value of this shift increases with decreasing group
velocity, in agreement with the theoretical predictions by Kocharovskaya,
Rostovtsev, and Scully [Phys. Rev. Lett. {\bf 86}, 628 (2001)].Comment: 4 pages 4 figures, submitted to PR
Lorentzian regularization and the problem of point-like particles in general relativity
The two purposes of the paper are (1) to present a regularization of the
self-field of point-like particles, based on Hadamard's concept of ``partie
finie'', that permits in principle to maintain the Lorentz covariance of a
relativistic field theory, (2) to use this regularization for defining a model
of stress-energy tensor that describes point-particles in post-Newtonian
expansions (e.g. 3PN) of general relativity. We consider specifically the case
of a system of two point-particles. We first perform a Lorentz transformation
of the system's variables which carries one of the particles to its rest frame,
next implement the Hadamard regularization within that frame, and finally come
back to the original variables with the help of the inverse Lorentz
transformation. The Lorentzian regularization is defined in this way up to any
order in the relativistic parameter 1/c^2. Following a previous work of ours,
we then construct the delta-pseudo-functions associated with this
regularization. Using an action principle, we derive the stress-energy tensor,
made of delta-pseudo-functions, of point-like particles. The equations of
motion take the same form as the geodesic equations of test particles on a
fixed background, but the role of the background is now played by the
regularized metric.Comment: 34 pages, to appear in J. Math. Phy
Equations of motion according to the asymptotic post-Newtonian scheme for general relativity in the harmonic gauge
The asymptotic scheme of post-Newtonian approximation defined for general
relativity (GR) in the harmonic gauge by Futamase & Schutz (1983) is based on a
family of initial data for the matter fields of a perfect fluid and for the
initial metric, defining a family of weakly self-gravitating systems. We show
that Weinberg's (1972) expansion of the metric and his general expansion of the
energy-momentum tensor , as well as his expanded equations for the
gravitational field and his general form of the expanded dynamical equations,
apply naturally to this family. Then, following the asymptotic scheme, we
derive the explicit form of the expansion of for a perfect fluid, and
the expanded fluid-dynamical equations. (These differ from those written by
Weinberg.) By integrating these equations in the domain occupied by a body, we
obtain a general form of the translational equations of motion for a 1PN
perfect-fluid system in GR. To put them into a tractable form, we use an
asymptotic framework for the separation parameter , by defining a family
of well-separated 1PN systems. We calculate all terms in the equations of
motion up to the order included. To calculate the 1PN correction
part, we assume that the Newtonian motion of each body is a rigid one, and that
the family is quasi-spherical, in the sense that in all bodies the inertia
tensor comes close to being spherical as . Apart from corrections
that cancel for exact spherical symmetry, there is in the final equations of
motion one additional term, as compared with the Lorentz-Droste
(Einstein-Infeld-Hoffmann) acceleration. This term depends on the spin of the
body and on its internal structure.Comment: 42 pages, no figure. Version accepted for publication in Physical
Review
On the Ginzburg-Landau Analysis of the Upper Critical Field Hc2 in MgB2
Temperature dependence of the upper critical field Hc2 (T) for the
superconducting magnesium diboride, MgB2, is studied in the vicinity of Tc by
using a two-band Ginzburg-Landau (G-L) theory. The temperature dependence of
Hc2 (T) near Tc exhibits a positive curvature. In addition, the calculated
temperature dependence and its higher order derivatives are also shown to be in
a good agreement with the experimental data. In analogy with the multi-band
character of Eliashberg microscopic theory, the positive curvature of Hc2 (T)
is described reasonably by solving the two-band of G-L theory.Comment: 14 pages, 2 figures, submitted to SUST November 200
On the nonsymmetric purely affine gravity
We review the vacuum purely affine gravity with the nonsymmetric connection
and metric. We also examine dynamical effects of the second Ricci tensor and
covariant second-rank tensors constructed from the torsion tensor in the
gravitational Lagrangian.Comment: 15 pages; published versio
Gravitation, electromagnetism and the cosmological constant in purely affine gravity
The Eddington Lagrangian in the purely affine formulation of general
relativity generates the Einstein equations with the cosmological constant. The
Ferraris-Kijowski purely affine Lagrangian for the electromagnetic field, which
has the form of the Maxwell Lagrangian with the metric tensor replaced by the
symmetrized Ricci tensor, is dynamically equivalent to the Einstein-Maxwell
Lagrangian in the metric formulation. We show that the sum of the two affine
Lagrangians is dynamically inequivalent to the sum of the analogous Lagrangians
in the metric-affine/metric formulation. We also show that such a construction
is valid only for weak electromagnetic fields. Therefore the purely affine
formulation that combines gravitation, electromagnetism and the cosmological
constant cannot be a simple sum of terms corresponding to separate fields.
Consequently, this formulation of electromagnetism seems to be unphysical,
unlike the purely metric and metric-affine pictures, unless the electromagnetic
field couples to the cosmological constant.Comment: 14 pages, extended and combined with gr-qc/0701176; published versio
Critical dynamics of ballistic and Brownian particles in a heterogeneous environment
The dynamic properties of a classical tracer particle in a random, disordered
medium are investigated close to the localization transition. For Lorentz
models obeying Newtonian and diffusive motion at the microscale, we have
performed large-scale computer simulations, demonstrating that universality
holds at long times in the immediate vicinity of the transition. The scaling
function describing the crossover from anomalous transport to diffusive motion
is found to vary extremely slowly and spans at least 5 decades in time. To
extract the scaling function, one has to allow for the leading universal
corrections to scaling. Our findings suggest that apparent power laws with
varying exponents generically occur and dominate experimentally accessible time
windows as soon as the heterogeneities cover a decade in length scale. We
extract the divergent length scales, quantify the spatial heterogeneities in
terms of the non-Gaussian parameter, and corroborate our results by a thorough
finite-size analysis.Comment: 14 page
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