59 research outputs found
Level-spacing distribution of a fractal matrix
We diagonalize numerically a Fibonacci matrix with fractal Hilbert space
structure of dimension We show that the density of states is
logarithmically normal while the corresponding level-statistics can be
described as critical since the nearest-neighbor distribution function
approaches the intermediate semi-Poisson curve. We find that the eigenvector
amplitudes of this matrix are also critical lying between extended and
localized.Comment: 6 pages, Latex file, 4 postscript files, published in Phys. Lett.
A289 pp 183-7 (2001
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.
One-Dimensional Extended States in Partially Disordered Planar Systems
We obtain analytically a continuum of one-dimensional ballistic extended
states in a two-dimensional disordered system, which consists of compactly
coupled random and pure square lattices. The extended states give a marginal
metallic phase with finite conductivity in a wide energy
range, whose boundaries define the mobility edges of a first-order
metal-insulator transition. We show current-voltage duality,
scaling of the conductivity in parallel magnetic field and
non-Fermi liquid properties when long-range electron-electron interactions are
included.Comment: 4 pages, revtex file, 3 postscript file
Quantum correlations from Brownian diffusion of chaotic level-spacings
Quantum chaos is linked to Brownian diffusion of the underlying quantum
energy level-spacing sequences. The level-spacings viewed as functions of their
order execute random walks which imply uncorrelated random increments of the
level-spacings while the integrability to chaos transition becomes a change
from Poisson to Gauss statistics for the level-spacing increments. This
universal nature of quantum chaotic spectral correlations is numerically
demonstrated for eigenvalues from random tight binding lattices and for zeros
of the Riemann zeta function.Comment: 4 pages, revtex file, 4 postscript file
Delocalization and spin-wave dynamics in ferromagnetic chains with long-range correlated random exchange
We study the one-dimensional quantum Heisenberg ferromagnet with exchange
couplings exhibiting long-range correlated disorder with power spectrum
proportional to , where is the wave-vector of the modulations
on the random coupling landscape. By using renormalization group, integration
of the equations of motion and exact diagonalization, we compute the spin-wave
localization length and the mean-square displacement of the wave-packet. We
find that, associated with the emergence of extended spin-waves in the
low-energy region for , the wave-packet mean-square displacement
changes from a long-time super-diffusive behavior for to a
long-time ballistic behavior for . At the vicinity of ,
the mobility edge separating the extended and localized phases is shown to
scale with the degree of correlation as .Comment: PRB to appea
Fractal Noise in Quantum Ballistic and Diffusive Lattice Systems
We demonstrate fractal noise in the quantum evolution of wave packets moving
either ballistically or diffusively in periodic and quasiperiodic tight-binding
lattices, respectively. For the ballistic case with various initial
superpositions we obtain a space-time self-affine fractal which
verify the predictions by Berry for "a particle in a box", in addition to
quantum revivals. For the diffusive case self-similar fractal evolution is also
obtained. These universal fractal features of quantum theory might be useful in
the field of quantum information, for creating efficient quantum algorithms,
and can possibly be detectable in scattering from nanostructures.Comment: 9 pages, 8 postscript figure
Conductance fluctuations and boundary conditions
The conductance fluctuations for various types for two-- and
three--dimensional disordered systems with hard wall and periodic boundary
conditions are studied, all the way from the ballistic (metallic) regime to the
localized regime. It is shown that the universal conductance fluctuations (UCF)
depend on the boundary conditions. The same holds for the metal to insulator
transition. The conditions for observing the UCF are also given.Comment: 4 pages RevTeX, 5 figures include
Delocalization in harmonic chains with long-range correlated random masses
We study the nature of collective excitations in harmonic chains with masses
exhibiting long-range correlated disorder with power spectrum proportional to
, where is the wave-vector of the modulations on the random
masses landscape. Using a transfer matrix method and exact diagonalization, we
compute the localization length and participation ratio of eigenmodes within
the band of allowed energies. We find extended vibrational modes in the
low-energy region for . In order to study the time evolution of an
initially localized energy input, we calculate the second moment of
the energy spatial distribution. We show that , besides being dependent
of the specific initial excitation and exhibiting an anomalous diffusion for
weakly correlated disorder, assumes a ballistic spread in the regime
due to the presence of extended vibrational modes.Comment: 6 pages, 9 figure
Statistical and Dynamical Study of Disease Propagation in a Small World Network
We study numerically statistical properties and dynamical disease propagation
using a percolation model on a one dimensional small world network. The
parameters chosen correspond to a realistic network of school age children. We
found that percolation threshold decreases as a power law as the short cut
fluctuations increase. We found also the number of infected sites grows
exponentially with time and its rate depends logarithmically on the density of
susceptibles. This behavior provides an interesting way to estimate the
serology for a given population from the measurement of the disease growing
rate during an epidemic phase. We have also examined the case in which the
infection probability of nearest neighbors is different from that of short
cuts. We found a double diffusion behavior with a slower diffusion between the
characteristic times.Comment: 12 pages LaTex, 10 eps figures, Phys.Rev.E Vol. 64, 056115 (2001
Symmetry, dimension and the distribution of the conductance at the mobility edge
The probability distribution of the conductance at the mobility edge,
, in different universality classes and dimensions is investigated
numerically for a variety of random systems. It is shown that is
universal for systems of given symmetry, dimensionality, and boundary
conditions. An analytical form of for small values of is discussed
and agreement with numerical data is observed. For , is
proportional to rather than .Comment: 4 pages REVTeX, 5 figures and 2 tables include
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