331 research outputs found
A random matrix decimation procedure relating to
Classical random matrix ensembles with orthogonal symmetry have the property
that the joint distribution of every second eigenvalue is equal to that of a
classical random matrix ensemble with symplectic symmetry. These results are
shown to be the case of a family of inter-relations between eigenvalue
probability density functions for generalizations of the classical random
matrix ensembles referred to as -ensembles. The inter-relations give
that the joint distribution of every -st eigenvalue in certain
-ensembles with is equal to that of another
-ensemble with . The proof requires generalizing a
conditional probability density function due to Dixon and Anderson.Comment: 19 pages, 1 figur
Scaling of Level Statistics at the Disorder-Induced Metal-Insulator Transition
The distribution of energy level separations for lattices of sizes up to
282828 sites is numerically calculated for the Anderson model.
The results show one-parameter scaling. The size-independent universality of
the critical level spacing distribution allows to detect with high precision
the critical disorder . The scaling properties yield the critical
exponent, , and the disorder dependence of the correlation
length.Comment: 11 pages (RevTex), 3 figures included (tar-compressed and uuencoded
using UUFILES), to appear in Phys.Rev. B 51 (Rapid Commun.
Anderson transitions in three-dimensional disordered systems with randomly varying magnetic flux
The Anderson transition in three dimensions in a randomly varying magnetic
flux is investigated in detail by means of the transfer matrix method with high
accuracy. Both, systems with and without an additional random scalar potential
are considered. We find a critical exponent of with random
scalar potential. Without it, is smaller but increases with the system
size and extrapolates within the error bars to a value close to the above. The
present results support the conventional classification of universality classes
due to symmetry.Comment: 4 pages, 2 figures, to appear in Phys. Rev.
Pfaffian Expressions for Random Matrix Correlation Functions
It is well known that Pfaffian formulas for eigenvalue correlations are
useful in the analysis of real and quaternion random matrices. Moreover the
parametric correlations in the crossover to complex random matrices are
evaluated in the forms of Pfaffians. In this article, we review the
formulations and applications of Pfaffian formulas. For that purpose, we first
present the general Pfaffian expressions in terms of the corresponding skew
orthogonal polynomials. Then we clarify the relation to Eynard and Mehta's
determinant formula for hermitian matrix models and explain how the evaluation
is simplified in the cases related to the classical orthogonal polynomials.
Applications of Pfaffian formulas to random matrix theory and other fields are
also mentioned.Comment: 28 page
Eigenvector localization for random band matrices with power law band width
It is shown that certain ensembles of random matrices with entries that
vanish outside a band around the diagonal satisfy a localization condition on
the resolvent which guarantees that eigenvectors have strong overlap with a
vanishing fraction of standard basis vectors, provided the band width
raised to a power remains smaller than the matrix size . For a
Gaussian band ensemble, with matrix elements given by i.i.d. centered Gaussians
within a band of width , the estimate holds.Comment: 30 pages; corrected typo
Spectral correlations : understanding oscillatory contributions
We give a different derivation of a relation obtained using a supersymmetric nonlinear sigma model by Andreev and Altshuler [Phys. Rev. Lett. 72, 902 (1995)], which connects smooth and oscillatory components of spectral correlation functions. We show that their result is not specific to the random matrix theory. Also, we show that despite an apparent contradiction, the results obtained using their formula are consistent with earlier perspectives on random matrix models
Universal Correlations of Coulomb Blockade Conductance Peaks and the Rotation Scaling in Quantum Dots
We show that the parametric correlations of the conductance peak amplitudes
of a chaotic or weakly disordered quantum dot in the Coulomb blockade regime
become universal upon an appropriate scaling of the parameter. We compute the
universal forms of this correlator for both cases of conserved and broken time
reversal symmetry. For a symmetric dot the correlator is independent of the
details in each lead such as the number of channels and their correlation. We
derive a new scaling, which we call the rotation scaling, that can be computed
directly from the dot's eigenfunction rotation rate or alternatively from the
conductance peak heights, and therefore does not require knowledge of the
spectrum of the dot. The relation of the rotation scaling to the level velocity
scaling is discussed. The exact analytic form of the conductance peak
correlator is derived at short distances. We also calculate the universal
distributions of the average level width velocity for various values of the
scaled parameter. The universality is illustrated in an Anderson model of a
disordered dot.Comment: 35 pages, RevTex, 6 Postscript figure
Scaling Analysis of Fluctuating Strength Function
We propose a new method to analyze fluctuations in the strength function
phenomena in highly excited nuclei. Extending the method of multifractal
analysis to the cases where the strength fluctuations do not obey power scaling
laws, we introduce a new measure of fluctuation, called the local scaling
dimension, which characterizes scaling behavior of the strength fluctuation as
a function of energy bin width subdividing the strength function. We discuss
properties of the new measure by applying it to a model system which simulates
the doorway damping mechanism of giant resonances. It is found that the local
scaling dimension characterizes well fluctuations and their energy scales of
fine structures in the strength function associated with the damped collective
motions.Comment: 22 pages with 9 figures; submitted to Phys. Rev.
The Ground State Energy of Dilute Bose Gas in Potentials with Positive Scattering Length
The leading term of the ground state energy/particle of a dilute gas of
bosons with mass in the thermodynamic limit is when
the density of the gas is , the interaction potential is non-negative and
the scattering length is positive. In this paper, we generalize the upper
bound part of this result to any interaction potential with positive scattering
length, i.e, and the lower bound part to some interaction potentials with
shallow and/or narrow negative parts.Comment: Latex 28 page
Dyson processes on the octonion algebra
We consider Brownian motion on symmetric matrices of octonions, and study the
law of the spectrum. Due to the fact that the octonion algebra is
nonassociative, the dimension of the matrices plays a special role. We provide
two specific models on octonions, which give some indication of the relation
between the multiplicity of eigenvalues and the exponent in the law of the
spectrum
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