313,323 research outputs found
Distribution of the spacing between two adjacent avoided crossings
We consider the frequency at which avoided crossings appear in an energy
level structure when an external field is applied to a quantum chaotic system.
The distribution of the spacing in the parameter between two adjacent avoided
crossings is investigated. Using a random matrix model, we find that the
distribution of these spacings is well fitted by a power-law distribution for
small spacings. The powers are 2 and 3 for the Gaussian orthogonal ensemble and
Gaussian unitary ensemble, respectively. We also find that the distributions
decay exponentially for large spacings. The distributions in concrete quantum
chaotic systems agree with those of the random matrix model.Comment: 11 page
Universality in Complex Networks: Random Matrix Analysis
We apply random matrix theory to complex networks. We show that nearest
neighbor spacing distribution of the eigenvalues of the adjacency matrices of
various model networks, namely scale-free, small-world and random networks
follow universal Gaussian orthogonal ensemble statistics of random matrix
theory. Secondly we show an analogy between the onset of small-world behavior,
quantified by the structural properties of networks, and the transition from
Poisson to Gaussian orthogonal ensemble statistics, quantified by Brody
parameter characterizing a spectral property. We also present our analysis for
a protein-protein interaction network in budding yeast.Comment: 4+ pages, 4 figures, to appear in PRE, major change in the paper
including titl
Spectral Statistics in the Quantized Cardioid Billiard
The spectral statistics in the strongly chaotic cardioid billiard are
studied. The analysis is based on the first 11000 quantal energy levels for odd
and even symmetry respectively. It is found that the level-spacing distribution
is in good agreement with the GOE distribution of random-matrix theory. In case
of the number variance and rigidity we observe agreement with the random-matrix
model for short-range correlations only, whereas for long-range correlations
both statistics saturate in agreement with semiclassical expectations.
Furthermore the conjecture that for classically chaotic systems the normalized
mode fluctuations have a universal Gaussian distribution with unit variance is
tested and found to be in very good agreement for both symmetry classes. By
means of the Gutzwiller trace formula the trace of the cosine-modulated heat
kernel is studied. Since the billiard boundary is focusing there are conjugate
points giving rise to zeros at the locations of the periodic orbits instead of
exclusively Gaussian peaks.Comment: 20 pages, uu-encoded ps.Z-fil
Spectral analysis of deformed random networks
We study spectral behavior of sparsely connected random networks under the
random matrix framework. Sub-networks without any connection among them form a
network having perfect community structure. As connections among the
sub-networks are introduced, the spacing distribution shows a transition from
the Poisson statistics to the Gaussian orthogonal ensemble statistics of random
matrix theory. The eigenvalue density distribution shows a transition to the
Wigner's semicircular behavior for a completely deformed network. The range for
which spectral rigidity, measured by the Dyson-Mehta statistics,
follows the Gaussian orthogonal ensemble statistics depends upon the
deformation of the network from the perfect community structure. The spacing
distribution is particularly useful to track very slight deformations of the
network from a perfect community structure, whereas the density distribution
and the statistics remain identical to the undeformed network. On
the other hand the statistics is useful for the larger deformation
strengths. Finally, we analyze the spectrum of a protein-protein interaction
network for Helicobacter, and compare the spectral behavior with those of the
model networks.Comment: accepted for publication in Phys. Rev. E (replaced with the final
version
Modelling gap-size distribution of parked cars using random-matrix theory
We apply the random-matrix theory to the car-parking problem. For this
purpose, we adopt a Coulomb gas model that associates the coordinates of the
gas particles with the eigenvalues of a random matrix. The nature of
interaction between the particles is consistent with the tendency of the
drivers to park their cars near to each other and in the same time keep a
distance sufficient for manoeuvring. We show that the recently measured
gap-size distribution of parked cars in a number of roads in central London is
well represented by the spacing distribution of a Gaussian unitary ensemble.Comment: 7 pages, 1 figur
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