25 research outputs found
Physical Bounds to the Entropy-Depolarization Relation in Random Light Scattering
We present a theoretical study of multi-mode scattering of light by optically
random media, using the Mueller-Stokes formalism which permits to encode all
the polarization properties of the scattering medium in a real
matrix. From this matrix two relevant parameters can be extracted: the
depolarizing power and the polarization entropy of the scattering
medium. By studying the relation between and , we find that {\em
all} scattering media must satisfy some {\em universal} constraints. These
constraints apply to both classical and quantum scattering processes. The
results obtained here may be especially relevant for quantum communication
applications, where depolarization is synonymous with decoherence.Comment: 4 pages, 2 figure
Spectral ergodicity and normal modes in ensembles of sparse matrices
We investigate the properties of sparse matrix ensembles with particular
regard for the spectral ergodicity hypothesis, which claims the identity of
ensemble and spectral averages of spectral correlators. An apparent violation
of the spectral ergodicity is observed. This effect is studied with the aid of
the normal modes of the random matrix spectrum, which describe fluctuations of
the eigenvalues around their average positions. This analysis reveals that
spectral ergodicity is not broken, but that different energy scales of the
spectra are examined by the two averaging techniques. Normal modes are shown to
provide a useful complement to traditional spectral analysis with possible
applications to a wide range of physical systems.Comment: 22 pages, 15 figure
Developments in Random Matrix Theory
In this preface to the Journal of Physics A, Special Edition on Random Matrix
Theory, we give a review of the main historical developments of random matrix
theory. A short summary of the papers that appear in this special edition is
also given.Comment: 22 pages, Late
Statistics of eigenfunctions in open chaotic systems: a perturbative approach
We investigate the statistical properties of the complexness parameter which
characterizes uniquely complexness (biorthogonality) of resonance eigenstates
of open chaotic systems. Specifying to the regime of isolated resonances, we
apply the random matrix theory to the effective Hamiltonian formalism and
derive analytically the probability distribution of the complexness parameter
for two statistical ensembles describing the systems invariant under time
reversal. For those with rigid spectra, we consider a Hamiltonian characterized
by a picket-fence spectrum without spectral fluctuations. Then, in the more
realistic case of a Hamiltonian described by the Gaussian Orthogonal Ensemble,
we reveal and discuss the r\^ole of spectral fluctuations
A maximum likelihood method to correct for missed levels based on the statistic
The statistic of Random Matrix Theory is defined as the average
of a set of random numbers , derived from a spectrum. The
distribution of these random numbers is used as the basis of a
maximum likelihood method to gauge the fraction of levels missed in an
experimental spectrum. The method is tested on an ensemble of depleted spectra
from the gaussian orthogonal ensemble (GOE), and accurately returned the
correct fraction of missed levels. Neutron resonance data and acoustic spectra
of an aluminum block were analyzed. All results were compared with an analysis
based on an established expression for for a depleted GOE
spectrum. The effects of intruder levels is examined, and seen to be very
similar to that of missed levels. Shell model spectra were seen to give the
same as the GOE.Comment: 23 pages, 13 figures, 1 tabl
Stochastic mean-field dynamics for fermions in the weak coupling limit
Assuming that the effect of the residual interaction beyond mean-field is
weak and has a short memory time, two approximate treatments of correlation in
fermionic systems by means of Markovian quantum jump are presented. A
simplified scenario for the introduction of fluctuations beyond mean-field is
first presented. In this theory, part of the quantum correlations between the
residual interaction and the one-body density matrix are neglected and jumps
occur between many-body densities formed of pairs of states where and are
antisymmetrized products of single-particle states. The underlying Stochastic
Mean-Field (SMF) theory is discussed and applied to the monopole vibration of a
spherical Ca nucleus under the influence of a statistical ensemble of
two-body contact interaction. This framework is however too simplistic to
account for both fluctuation and dissipation. In the second part of this work,
an alternative quantum jump method is obtained without making the approximation
on quantum correlations. Restricting to two particles-two holes residual
interaction, the evolution of the one-body density matrix of a correlated
system is transformed into a Lindblad equation. The associated dissipative
dynamics can be simulated by quantum jumps between densities written as is a normalized Slater determinant. The
associated stochastic Schroedinger equation for single-particle wave-functions
is given.Comment: Enlarged version, 10 pages, 2 figure