1,056 research outputs found
Anderson transition in the three dimensional symplectic universality class
We study the Anderson transition in the SU(2) model and the Ando model. We
report a new precise estimate of the critical exponent for the symplectic
universality class of the Anderson transition. We also report numerical
estimation of the function.Comment: 4 pages, 5 figure
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
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
Probability distribution of the conductance at the mobility edge
Distribution of the conductance P(g) at the critical point of the
metal-insulator transition is presented for three and four dimensional
orthogonal systems. The form of the distribution is discussed. Dimension
dependence of P(g) is proven. The limiting cases and are
discussed in detail and relation in the limit is proven.Comment: 4 pages, 3 .eps figure
What is the right form of the probability distribution of the conductance at the mobility edge?
The probability distribution of the conductance Pc(g) at the Anderson
critical point is calculated. It is find that Pc(g) has a dip at small g in
agreement with epsilon expansion results. The Pc(g) for the 3d system is quite
different from the 2d quantum critical point of the integer quantum Hall
effect. The universality or not of these distributions is of central importance
to the field of disordered systems.Comment: 1 page, 1 figure submitted to Phys. Rev. Lett. (Comment
Renormalizing Rectangles and Other Topics in Random Matrix Theory
We consider random Hermitian matrices made of complex or real
rectangular blocks, where the blocks are drawn from various ensembles. These
matrices have pairs of opposite real nonvanishing eigenvalues, as well as
zero eigenvalues (for .) These zero eigenvalues are ``kinematical"
in the sense that they are independent of randomness. We study the eigenvalue
distribution of these matrices to leading order in the large limit, in
which the ``rectangularity" is held fixed. We apply a variety of
methods in our study. We study Gaussian ensembles by a simple diagrammatic
method, by the Dyson gas approach, and by a generalization of the Kazakov
method. These methods make use of the invariance of such ensembles under the
action of symmetry groups. The more complicated Wigner ensemble, which does not
enjoy such symmetry properties, is studied by large renormalization
techniques. In addition to the kinematical -function spike in the
eigenvalue density which corresponds to zero eigenvalues, we find for both
types of ensembles that if is held fixed as , the
non-zero eigenvalues give rise to two separated lobes that are located
symmetrically with respect to the origin. This separation arises because the
non-zero eigenvalues are repelled macroscopically from the origin. Finally, we
study the oscillatory behavior of the eigenvalue distribution near the
endpoints of the lobes, a behavior governed by Airy functions. As the lobes come closer, and the Airy oscillatory behavior near the endpoints
that are close to zero breaks down. We interpret this breakdown as a signal
that drives a cross over to the oscillation governed by Bessel
functions near the origin for matrices made of square blocks.Comment: LateX, 34 pages, 3 ps figure
The Anderson Transition in Two-Dimensional Systems with Spin-Orbit Coupling
We report a numerical investigation of the Anderson transition in
two-dimensional systems with spin-orbit coupling. An accurate estimate of the
critical exponent for the divergence of the localization length in this
universality class has to our knowledge not been reported in the literature.
Here we analyse the SU(2) model. We find that for this model corrections to
scaling due to irrelevant scaling variables may be neglected permitting an
accurate estimate of the exponent
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