3,084 research outputs found
Quasi-isotropic approximation of geometric optics
Modified geometric optics method for solution of Maxwell equation
Stokes-vector evolution in a weakly anisotropic inhomogeneous medium
Equation for evolution of the four-component Stokes vector in weakly
anisotropic and smoothly inhomogeneous media is derived on the basis of
quasi-isotropic approximation of the geometrical optics method, which provides
consequent asymptotic solution of Maxwell equations. Our equation generalizes
previous results, obtained for the normal propagation of electromagnetic waves
in stratified media. It is valid for curvilinear rays with torsion and is
capable to describe normal modes conversion in the inhomogeneous media.
Remarkably, evolution of the Stokes vector is described by the
Bargmann-Michel-Telegdi equation for relativistic spin precession, whereas the
equation for the three-component Stokes vector resembles the Landau-Lifshitz
equation for spin precession in ferromegnetic systems. General theory is
applied for analysis of polarization evolution in a magnetized plasma. We also
emphasize fundamental features of the non-Abelian polarization evolution in
anisotropic inhomogeneous media and illustrate them by simple examples.Comment: 16 pages, 3 figures, to appear in J. Opt. Soc. Am.
Properties of voids in the Local Volume
Current explanation of the overabundance of dark matter subhalos in the Local
Group (LG) indicates that there maybe a limit on mass of a halo, which can host
a galaxy. This idea can be tested using voids in the distribution of galaxies:
at some level small voids should not contain any (even dwarf) galaxies. We use
observational samples complete to M_B=-12 with distances less than 8 Mpc to
construct the void function (VF): the distribution of sizes of voids empty of
any galaxies. There are ~ 30 voids with sizes ranging from 1 to 5 Mpc. We also
study the distribution of dark matter halos in very high resolution simulations
of the LCDM model. The theoretical VF matches the observations remarkably well
only if we use halos with circular velocities larger than 45 +/- 10 km/s. This
agrees with the Local Group predictions. Small voids look quite similar to heir
giant cousins: the density has a minimum at the center of a void and it
increases as we get closer to the border. Thus, both the Local Group data and
the nearby voids indicate that isolated halos below 45 +/- 10 km/s must not
host galaxies and that small (few Mpc) voids are truly dark.Comment: 5 pages 1 figure. To appear in proceedings of the conference
"Galaxies in the Local Volume", Sydney, 8 to 13 July 200
On problem of polarization tomography, I
The polarization tomography problem consists of recovering a matrix function
f from the fundamental matrix of the equation
known for every geodesic of a given Riemannian metric. Here
is the orthogonal projection onto the hyperplan
. The problem arises in optical tomography of slightly
anisotropic media. The local uniqueness theorem is proved: a - small
function f can be recovered from the data uniquely up to a natural obstruction.
A partial global result is obtained in the case of the Euclidean metric on
Energy level dynamics in systems with weakly multifractal eigenstates: equivalence to 1D correlated fermions
It is shown that the parametric spectral statistics in the critical random
matrix ensemble with multifractal eigenvector statistics are identical to the
statistics of correlated 1D fermions at finite temperatures. For weak
multifractality the effective temperature of fictitious 1D fermions is
proportional to (1-d_{n})/n, where d_{n} is the fractal dimension found from
the n-th moment of inverse participation ratio. For large energy and parameter
separations the fictitious fermions are described by the Luttinger liquid model
which follows from the Calogero-Sutherland model. The low-temperature
asymptotic form of the two-point equal-parameter spectral correlation function
is found for all energy separations and its relevance for the low temperature
equal-time density correlations in the Calogero-Sutherland model is
conjectured.Comment: 4 pages, Revtex, final journal versio
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