331 research outputs found
Magnetic-Field Dependence of the Localization Length in Anderson Insulators
Using the conventional scaling approach as well as the renormalization group
analysis in dimensions, we calculate the localization length
in the presence of a magnetic field . For the quasi 1D case the
results are consistent with a universal increase of by a numerical
factor when the magnetic field is in the range
\ell\ll{\ell_{\!{_H}}}\alt\xi(0), is the mean free path,
is the magnetic length . However, for
where the magnetic field does cause delocalization there is no
universal relation between and . The effect of spin-orbit
interaction is briefly considered as well.Comment: 4 pages, revtex, no figures; to be published in Europhysics Letter
Conductance length autocorrelation in quasi one-dimensional disordered wires
Employing techniques recently developed in the context of the Fokker--Planck
approach to electron transport in disordered systems we calculate the
conductance length correlation function
for quasi 1d wires. Our result is valid for arbitrary lengths L and .
In the metallic limit the correlation function is given by a squared
Lorentzian. In the localized regime it decays exponentially in both L and
. The correlation length is proportional to L in the metallic regime
and saturates at a value approximately given by the localization length
as .Comment: 23 pages, Revtex, two figure
Analytical Results for Random Band Matrices with Preferential Basis
Using the supersymmetry method we analytically calculate the local density of
states, the localiztion length, the generalized inverse participation ratios,
and the distribution function of eigenvector components for the superposition
of a random band matrix with a strongly fluctuating diagonal matrix. In this
way we extend previously known results for ordinary band matrices to the class
of random band matrices with preferential basis. Our analytical results are in
good agreement with (but more general than) recent numerical findings by
Jacquod and Shepelyansky.Comment: 8 pages RevTex and 1 Figure, both uuencode
Ballistic transport in disordered graphene
An analytic theory of electron transport in disordered graphene in a
ballistic geometry is developed. We consider a sample of a large width W and
analyze the evolution of the conductance, the shot noise, and the full
statistics of the charge transfer with increasing length L, both at the Dirac
point and at a finite gate voltage. The transfer matrix approach combined with
the disorder perturbation theory and the renormalization group is used. We also
discuss the crossover to the diffusive regime and construct a ``phase diagram''
of various transport regimes in graphene.Comment: 23 pages, 10 figure
Localization length in Dorokhov's microscopic model of multichannel wires
We derive exact quantum expressions for the localization length for
weak disorder in two- and three chain tight-binding systems coupled by random
nearest-neighbour interchain hopping terms and including random energies of the
atomic sites. These quasi-1D systems are the two- and three channel versions of
Dorokhov's model of localization in a wire of periodically arranged atomic
chains. We find that for the considered systems with
, where is Thouless' quantum expression for the inverse
localization length in a single 1D Anderson chain, for weak disorder. The
inverse localization length is defined from the exponential decay of the
two-probe Landauer conductance, which is determined from an earlier transfer
matrix solution of the Schr\"{o}dinger equation in a Bloch basis. Our exact
expressions above differ qualitatively from Dorokhov's localization length
identified as the length scaling parameter in his scaling description of the
distribution of the participation ratio. For N=3 we also discuss the case where
the coupled chains are arranged on a strip rather than periodically on a tube.
From the transfer matrix treatment we also obtain reflection coefficients
matrices which allow us to find mean free paths and to discuss their relation
to localization lengths in the two- and three channel systems
How the recent BABAR data for P to \gamma\gamma* affect the Standard Model predictions for the rare decays P to l+l-
Measuring the lepton anomalous magnetic moments and the rare decays
of light pseudoscalar mesons into lepton pairs , serve as
important tests of the Standard Model. To reduce the theoretical uncertainty in
the standard model predictions, the data on the charge and transition form
factors of the light pseudoscalar mesons play a significant role. Recently, new
data on the behavior of the transition form factors at
large momentum transfer were supplied by the BABAR collaboration. There are
several problems with the theoretical interpretation of these data: 1) An
unexpectedly slow decrease of the pion transition form factor at high momenta,
2) the qualitative difference in the behavior of the pion form factor and the
and form factors at high momenta, 3) the inconsistency of
the measured ratio of the and form factors with the
predicted one. We comment on the influence of the new BABAR data on the rare
decay branchings.Comment: 11 pages, 3 figure
Localization fom conductance in few-channel disordered wires
We study localization in two- and three channel quasi-1D systems using
multichain tight-binding Anderson models with nearest-neighbour interchain
hopping. In the three chain case we discuss both the case of free- and that of
periodic boundary conditions between the chains. The finite disordered wires
are connected to ideal leads and the localization length is defined from the
Landauer conductance in terms of the transmission coefficients matrix. The
transmission- and reflection amplitudes in properly defined quantum channels
are obtained from S-matrices constructed from transfer matrices in Bloch wave
bases for the various quasi-1D systems. Our exact analytic expressions for
localization lengths for weak disorder reduce to the Thouless expression for 1D
systems in the limit of vanishing interchain hopping. For weak interchain
hopping the localization length decreases with respect to the 1D value in all
three cases. In the three-channel cases it increases with interchain hopping
over restricted domains of large hopping
Conductance of 1D quantum wires with anomalous electron-wavefunction localization
We study the statistics of the conductance through one-dimensional
disordered systems where electron wavefunctions decay spatially as for , being a constant. In
contrast to the conventional Anderson localization where and the conductance statistics is determined by a single
parameter: the mean free path, here we show that when the wave function is
anomalously localized () the full statistics of the conductance is
determined by the average and the power . Our theoretical
predictions are verified numerically by using a random hopping tight-binding
model at zero energy, where due to the presence of chiral symmetry in the
lattice there exists anomalous localization; this case corresponds to the
particular value . To test our theory for other values of
, we introduce a statistical model for the random hopping in the tight
binding Hamiltonian.Comment: 6 pages, 8 figures. Few changes in the presentation and references
updated. Published in PRB, Phys. Rev. B 85, 235450 (2012
Interaction-induced delocalization of two particles in a random potential: Scaling properties
The localization length for coherent propagation of two interacting
particles in a random potential is studied using a novel and efficient
numerical method. We find that the enhancement of over the one-particle
localization length satisfies the scaling relation
, where is the interaction strength and
the level spacing of a wire of length . The scaling
function is linear over the investigated parameter range. This implies that
increases faster with than previously predicted. We also study a
novel mapping of the problem to a banded-random-matrix model.Comment: 5 pages and two figures in a uuencoded, compressed tar file; uses
revtex and psfig.sty (included); substantial revision of a previous version
of the paper including newly discovered scaling behavio
Exploring Level Statistics from Quantum Chaos to Localization with the Autocorrelation Function of Spectral Determinants
The autocorrelation function of spectral determinants (ASD) is used to
characterize the discrete spectrum of a phase coherent quasi- 1- dimensional,
disordered wire as a function of its length L in a finite, weak magnetic field.
An analytical function is obtained depending only on the dimensionless
conductance g= xi/L where xi is the localization length, the scaled frequency
x= omega/Delta, where Delta is the average level spacing of the wire, and the
global symmetry of the system. A metal- insulator crossover is observed,
showing that information on localization is contained in the disorder averaged
ASD.Comment: 4 pages, 3 figure
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