18,084 research outputs found
Quasiclassical Random Matrix Theory
We directly combine ideas of the quasiclassical approximation with random
matrix theory and apply them to the study of the spectrum, in particular to the
two-level correlator. Bogomolny's transfer operator T, quasiclassically an NxN
unitary matrix, is considered to be a random matrix. Rather than rejecting all
knowledge of the system, except for its symmetry, [as with Dyson's circular
unitary ensemble], we choose an ensemble which incorporates the knowledge of
the shortest periodic orbits, the prime quasiclassical information bearing on
the spectrum. The results largely agree with expectations but contain novel
features differing from other recent theories.Comment: 4 pages, RevTex, submitted to Phys. Rev. Lett., permanent e-mail
[email protected]
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
Random matrix theory within superstatistics
We propose a generalization of the random matrix theory following the basic
prescription of the recently suggested concept of superstatistics. Spectral
characteristics of systems with mixed regular-chaotic dynamics are expressed as
weighted averages of the corresponding quantities in the standard theory
assuming that the mean level spacing itself is a stochastic variable. We
illustrate the method by calculating the level density, the
nearest-neighbor-spacing distributions and the two-level correlation functions
for system in transition from order to chaos. The calculated spacing
distribution fits the resonance statistics of random binary networks obtained
in a recent numerical experiment.Comment: 20 pages, 6 figure
Staggered chiral random matrix theory
We present a random matrix theory (RMT) for the staggered lattice QCD Dirac
operator. The staggered RMT is equivalent to the zero-momentum limit of the
staggered chiral Lagrangian and includes all taste breaking terms at their
leading order. This is an extension of previous work which only included some
of the taste breaking terms. We will also present some results for the taste
breaking contributions to the partition function and the Dirac eigenvalues.Comment: 12 pages, 7 figures, v2 has minor edits and corrections to some
equations to match published versio
Random matrix theory and
We suggest that the spectral properties near zero virtuality of three
dimensional QCD, follow from a Hermitean random matrix model. The exact
spectral density is derived for this family of random matrix models both for
even and odd number of fermions. New sum rules for the inverse powers of the
eigenvalues of the Dirac operator are obtained. The issue of anomalies in
random matrix theories is discussed.Comment: 10p., SUNY-NTG-94/1
Spectral Statistics Beyond Random Matrix Theory
Using a nonperturbative approach we examine the large frequency asymptotics
of the two-point level density correlator in weakly disordered metallic grains.
This allows us to study the behavior of the two-level structure factor close to
the Heisenberg time. We find that the singularities (present for random matrix
ensembles) are washed out in a grain with a finite conductance. The results are
nonuniversal (they depend on the shape of the grain and on its conductance),
though they suggest a generalization for any system with finite Heisenberg
time.Comment: Uuencoded file with two eps figures, 10 pages
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