18 research outputs found
Statistics of level spacing of geometric resonances in random binary composites
We study the statistics of level spacing of geometric resonances in the
disordered binary networks. For a definite concentration within the
interval , numerical calculations indicate that the unfolded level
spacing distribution and level number variance have the
general features. It is also shown that the short-range fluctuation and
long-range spectral correlation lie between the profiles of the
Poisson ensemble and Gaussion orthogonal ensemble (GOE). At the percolation
threshold , crossover behavior of functions and is
obtained, giving the finite size scaling of mean level spacing and
mean level number , which obey the scaling laws, and .Comment: 11 pages, 7 figures,submitted to Phys. Rev.
Metal-insulator transition in two-dimensional disordered systems with power-law transfer terms
We investigate a disordered two-dimensional lattice model for noninteracting
electrons with long-range power-law transfer terms and apply the method of
level statistics for the calculation of the critical properties. The
eigenvalues used are obtained numerically by direct diagonalization. We find a
metal-insulator transition for a system with orthogonal symmetry. The exponent
governing the divergence of the correlation length at the transition is
extracted from a finite size scaling analysis and found to be . The critical eigenstates are also analyzed and the distribution of the
generalized multifractal dimensions is extrapolated.Comment: 4 pages with 4 figures, printed version: PRB, Rapid Communication
Magnetotransport in inhomogeneous magnetic fields
Quantum transport in inhomogeneous magnetic fields is investigated
numerically in two-dimensional systems using the equation of motion method. In
particular, the diffusion of electrons in random magnetic fields in the
presence of additional weak uniform magnetic fields is examined. It is found
that the conductivity is strongly suppressed by the additional uniform magnetic
field and saturates when the uniform magnetic field becomes on the order of the
fluctuation of the random magnetic field. The value of the conductivity at this
saturation is found to be insensitive to the magnitude of the fluctuation of
the random field. The effect of random potential on the magnetoconductance is
also discussed.Comment: 5 pages, 5 figure
Critical statistics in a power-law random banded matrix ensemble
We investigate the statistical properties of the eigenvalues and eigenvectors
in a random matrix ensemble with . It is known that
this model shows a localization-delocalization transition (LDT) as a function
of the parameter . The model is critical at and the eigenstates
are multifractals. Based on numerical simulations we demonstrate that the
spectral statistics at criticality differs from semi-Poisson statistics which
is expected to be a general feature of systems exhibiting a LDT or `weak
chaos'.Comment: 4 pages in PS including 5 figure
Energy-level statistics at the metal-insulator transition in anisotropic systems
We study the three-dimensional Anderson model of localization with
anisotropic hopping, i.e. weakly coupled chains and weakly coupled planes. In
our extensive numerical study we identify and characterize the metal-insulator
transition using energy-level statistics. The values of the critical disorder
are consistent with results of previous studies, including the
transfer-matrix method and multifractal analysis of the wave functions.
decreases from its isotropic value with a power law as a function of
anisotropy. Using high accuracy data for large system sizes we estimate the
critical exponent . This is in agreement with its value in the
isotropic case and in other models of the orthogonal universality class. The
critical level statistics which is independent of the system size at the
transition changes from its isotropic form towards the Poisson statistics with
increasing anisotropy.Comment: 22 pages, including 8 figures, revtex few typos corrected, added
journal referenc
Levitation of quantum Hall critical states in a lattice model with spatially correlated disorder
The fate of the current carrying states of a quantum Hall system is
considered in the situation when the disorder strength is increased and the
transition from the quantum Hall liquid to the Hall insulator takes place. We
investigate a two-dimensional lattice model with spatially correlated disorder
potentials and calculate the density of states and the localization length
either by using a recursive Green function method or by direct diagonalization
in connection with the procedure of level statistics. From the knowledge of the
energy and disorder dependence of the localization length and the density of
states (DOS) of the corresponding Landau bands, the movement of the current
carrying states in the disorder--energy and disorder--filling-factor plane can
be traced by tuning the disorder strength.
We show results for all sub-bands, particularly the traces of the Chern and
anti-Chern states as well as the peak positions of the DOS. For small disorder
strength we recover the well known weak levitation of the critical states,
but we also reveal, for larger , the strong levitation of these states
across the Landau gaps without merging. We find the behavior to be similar for
exponentially, Gaussian, and Lorentzian correlated disorder potentials. Our
study resolves the discrepancies of previously published work in demonstrating
the conflicting results to be only special cases of a general lattice model
with spatially correlated disorder potentials.
To test whether the mixing between consecutive Landau bands is the origin of
the observed floating, we truncate the Hilbert space of our model Hamiltonian
and calculate the behavior of the current carrying states under these
restricted conditions.Comment: 10 pages, incl. 13 figures, accepted for publication in PR