2,364 research outputs found
The Level Spacing Distribution Near the Anderson Transition
For a disordered system near the Anderson transition we show that the
nearest-level-spacing distribution has the asymptotics for s\gg \av{s}\equiv 1 which is universal and intermediate
between the Gaussian asymptotics in a metal and the Poisson in an insulator.
(Here the critical exponent and the numerical coefficient
depend only on the dimensionality ). It is obtained by mapping the energy
level distribution to the Gibbs distribution for a classical one-dimensional
gas with a pairwise interaction. The interaction, consistent with the universal
asymptotics of the two-level correlation function found previously, is proved
to be the power-law repulsion with the exponent .Comment: REVTeX, 8 pages, no figure
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
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