435 research outputs found
Nonchiral Edge States at the Chiral Metal Insulator Transition in Disordered Quantum Hall Wires
The quantum phase diagram of disordered wires in a strong magnetic field is
studied as a function of wire width and energy. The two-terminal conductance
shows zero-temperature discontinuous transitions between exactly integer
plateau values and zero. In the vicinity of this transition, the chiral
metal-insulator transition (CMIT), states are identified that are
superpositions of edge states with opposite chirality. The bulk contribution of
such states is found to decrease with increasing wire width. Based on exact
diagonalization results for the eigenstates and their participation ratios, we
conclude that these states are characteristic for the CMIT, have the appearance
of nonchiral edges states, and are thereby distinguishable from other states in
the quantum Hall wire, namely, extended edge states, two-dimensionally (2D)
localized, quasi-1D localized, and 2D critical states.Comment: replaced with revised versio
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
Phase Transition in a Model with Non-Compact Symmetry on Bethe Lattice and the Replica Limit
We solve nonlinear vector model on Bethe lattice and show that it
exhibits a transition from ordered to disordered state for . If
the replica limit is taken carefully, the model is shown to reduce to
the corresponding supersymmetric model. The latter was introduced by Zirnbauer
as a toy model for the Anderson localization transition. We argue thus that the
non-compact replica models describe correctly the Anderson transition features.
This should be contrasted to their failure in the case of the level correlation
problem.Comment: 21 pages, REVTEX, 2 Postscript figures, uses epsf styl
Effects of fluctuations and Coulomb interaction on the transition temperature of granular superconductors
We investigate the suppression of superconducting transition temperature in
granular metallic systems due to (i) fluctuations of the order parameter
(bosonic mechanism) and (ii) Coulomb repulsion (fermionic mechanism) assuming
large tunneling conductance between the grains . We find the
correction to the superconducting transition temperature for 3 granular
samples and films. We demonstrate that if the critical temperature , where is the mean level spacing in a single grain the bosonic
mechanism is the dominant mechanism of the superconductivity suppression, while
for critical temperatures the suppression of
superconductivity is due to the fermionic mechanism.Comment: 12 pages, 9 figures, several sections clarifying the details of our
calculations are adde
Two-scale localization in disordered wires in a magnetic field
Calculating the density-density correlation function for disordered wires, we
study localization properties of wave functions in a magnetic field. The
supersymmetry technique combined with the transfer matrix method is used. It is
demonstrated that at arbitrarily weak magnetic field the far tail of the wave
functions decays with the length , where and are the localization lengths in the absence of a
magnetic field and in a strong magnetic field, respectively. At shorter
distances, the decay of the wave functions is characterized by the length
. Increasing the magnetic field broadens the region of the decay
with the length , leading finally to the decay with at all distances. In other words, the crossover between the orthogonal
and unitary ensembles in disordered wires is characterized by two localization
lengths. This peculiar behavior must result in two different temperature
regimes in the hopping conductivity with the boundary between them depending on
the magnetic field.Comment: 4 page
Long-range correlations in the wave functions of chaotic systems
We study correlations of the amplitudes of wave functions of a chaotic system
at large distances. For this purpose, a joint distribution function of the
amplitudes at two distant points in a sample is calculated analytically using
the supersymmetry technique. The result shows that, although in the limit of
the orthogonal and unitary symmetry classes the correlations vanish, they are
finite through the entire crossover regime and may be reduced only by
localization effects.Comment: 4 pages RevTex + 2 fig
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
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
Anderson localization from the replica formalism
We study Anderson localization in quasi--one--dimensional disordered wires
within the framework of the replica --model. Applying a semiclassical
approach (geodesic action plus Gaussian fluctuations) recently introduced
within the context of supersymmetry by Lamacraft, Simons and Zirnbauer
\cite{LSZ}, we compute the {\em exact} density of transmission matrix
eigenvalues of superconducting wires (of symmetry class I.) For the unitary
class of metallic systems (class ) we are able to obtain the density
function, save for its large transmission tail.Comment: 4 pages, 1 figur
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
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