250 research outputs found
Scaling and the center of band anomaly in a one-dimensional Anderson model with diagonal disorder
We resolve the problem of the violation of single parameter scaling at the
zero energy of the Anderson tight-binding model with diagonal disorder. It
follows from the symmetry properties of the tight-binding Hamiltonian that this
spectral point is in fact a boundary between two adjacent bands. The states in
the vicinity of this energy behave similarly to states at other band
boundaries, which are known to violate single parameter scaling.Comment: revised version, 4 pages, 2 figures, revte
Scaling of the localization length in linear electronic and vibrational systems with long-range correlated disorder
The localization lengths of long-range correlated disordered chains are
studied for electronic wavefunctions in the Anderson model and for vibrational
states. A scaling theory close to the band edge is developed in the Anderson
model and supported by numerical simulations. This scaling theory is mapped
onto the vibrational case at small frequencies. It is shown that for small
frequencies, unexpectateley the localization length is smaller for correlated
than for uncorrelated chains.Comment: to be published in PRB, 4 pages, 2 Figure
Low density expansion for Lyapunov exponents
In some quasi-one-dimensional weakly disordered media, impurities are large
and rare rather than small and dense. For an Anderson model with a low density
of strong impurities, a perturbation theory in the impurity density is
developed for the Lyapunov exponent and the density of states. The Lyapunov
exponent grows linearly with the density. Anomalies of the Kappus-Wegner type
appear for all rational quasi-momenta even in lowest order perturbation theory
1D quantum models with correlated disorder vs. classical oscillators with coloured noise
We perform an analytical study of the correspondence between a classical
oscillator with frequency perturbed by a coloured noise and the one-dimensional
Anderson-type model with correlated diagonal disorder. It is rigorously shown
that localisation of electronic states in the quantum model corresponds to
exponential divergence of nearby trajectories of the classical random
oscillator. We discuss the relation between the localisation length for the
quantum model and the rate of energy growth for the stochastic oscillator.
Finally, we examine the problem of electron transmission through a finite
disordered barrier by considering the evolution of the classical oscillator.Comment: 23 pages, LaTeX fil
Random Fibonacci Sequences
Solutions to the random Fibonacci recurrence x_{n+1}=x_{n} + or - Bx_{n-1}
decrease (increase) exponentially, x_{n} = exp(lambda n), for sufficiently
small (large) B. In the limits B --> 0 and B --> infinity, we expand the
Lyapunov exponent lambda(B) in powers of B and B^{-1}, respectively. For the
classical case of we obtain exact non-perturbative results. In
particular, an invariant measure associated with Ricatti variable
r_n=x_{n+1}/x_{n} is shown to exhibit plateaux around all rational.Comment: 11 Pages (Multi-Column); 3 EPS Figures ; Submitted to J. Phys.
Anderson localization as a parametric instability of the linear kicked oscillator
We rigorously analyse the correspondence between the one-dimensional standard
Anderson model and a related classical system, the `kicked oscillator' with
noisy frequency. We show that the Anderson localization corresponds to a
parametric instability of the oscillator, with the localization length
determined by an increment of the exponential growth of the energy. Analytical
expression for a weak disorder is obtained, which is valid both inside the
energy band and at the band edge.Comment: 7 pages, Revtex, no figures, submitted to Phys. Rev.
Single parameter scaling in one-dimensional localization revisited
The variance of the Lyapunov exponent is calculated exactly in the
one-dimensional Anderson model with random site energies distributed according
to the Cauchy distribution. We find a new significant scaling parameter in the
system, and derive an exact analytical criterion for single parameter scaling
which differs from the commonly used condition of phase randomization. The
results obtained are applied to the Kronig-Penney model with the potential in
the form of periodically positioned -functions with random strength.Comment: Phys. Rev. Lett. 84, 2678 (2000
Persistent Currents in Multichannel Interacting Systems
Persistent currents of disordered multichannel mesoscopic rings of spinless
interacting fermions threaded by a magnetic flux are calculated using exact
diagonalizations and self-consistent Hartree-Fock methods. The validity of the
Hartree-Fock approximation is controled by a direct comparison with the exact
results on small clusters. For sufficiently large disorder
(diffusive regime), the effect of repulsive interactions on the current
distribution is to slightly decrease its width (mean square current) but to
{\it increase} its mean value (mean current). This effect is stronger in the
case of a long range repulsion. Our results suggest that the coupling between
the chains is essential to understand the large currents observed
experimentally.Comment: Revised version, uuencoded compressed file including fig
Failure of single-parameter scaling of wave functions in Anderson localization
We show how to use properties of the vectors which are iterated in the
transfer-matrix approach to Anderson localization, in order to generate the
statistical distribution of electronic wavefunction amplitudes at arbitary
distances from the origin of disordered systems. For
our approach is shown to reproduce exact diagonalization results
available in the literature. In , where strips of width sites
were used, attempted fits of gaussian (log-normal) forms to the wavefunction
amplitude distributions result in effective localization lengths growing with
distance, contrary to the prediction from single-parameter scaling theory. We
also show that the distributions possess a negative skewness , which is
invariant under the usual histogram-collapse rescaling, and whose absolute
value increases with distance. We find for the
range of parameters used in our study, .Comment: RevTeX 4, 6 pages, 4 eps figures. Phys. Rev. B (final version, to be
published
Suppression of Persistent Currents in 1-D Disordered Rings by Coulomb Interaction
Effects of Coulomb interaction on persistent currents in disordered
one-dimensional rings are numerically investigated. First of all effectiveness
of the Hartree-Fock approximation is established on small systems. Then the
calculations are done for systems with 40 electrons in 100 sites. It is found
that the amplitude of the average persistent current in the diffusive regime is
suppressed as the strength of the Coulomb interaction increases. The
suppression of the current is stronger in larger rings than in smaller ones.
The enhancement of the current by the electron-electron interaction was not
observed in the diffusive regime.Comment: 9 pages (RevTeX), 4 figures available upon request
([email protected]), KCMG-preprint-HK
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