875,790 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
High-Dimensional Random Fields and Random Matrix Theory
Our goal is to discuss in detail the calculation of the mean number of
stationary points and minima for random isotropic Gaussian fields on a sphere
as well as for stationary Gaussian random fields in a background parabolic
confinement. After developing the general formalism based on the
high-dimensional Kac-Rice formulae we combine it with the Random Matrix Theory
(RMT) techniques to perform analysis of the random energy landscape of spin
spherical spinglasses and a related glass model, both displaying a
zero-temperature one-step replica symmetry breaking glass transition as a
function of control parameters (e.g. a magnetic field or curvature of the
confining potential). A particular emphasis of the presented analysis is on
understanding in detail the picture of "topology trivialization" (in the sense
of drastic reduction of the number of stationary points) of the landscape which
takes place in the vicinity of the zero-temperature glass transition in both
models. We will reveal the important role of the GOE "edge scaling" spectral
region and the Tracy-Widom distribution of the maximal eigenvalue of GOE
matrices for providing an accurate quantitative description of the universal
features of the topology trivialization scenario.Comment: 40 pages; 2 figures; In this version the original lecture notes are
converted to an article format, new Eqs. (82)-(85) and Appendix about
anisotropic fields added, noticed misprints corrected, references updated.
references update
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