146 research outputs found
Spatial and Spectral Multifractality of the Local Density of States at the Mobility Edge
We performed numerical calculations of the local density of states (LDOS) at
disorder induced localization-delocalization transitions. The LDOS defines a
spatial measure for fixed energy and a spectral measure for fixed position. At
the mobility edge both measures are multifractal and their generalized
dimensions and are found to be proportional:
, where is the dimension of the system. This
observation is consistent with the identification of the frequency-dependent
length scale as an effective system size. The
calculations are performed for two- and three-dimensional dynamical network
models with local time evolution operators. The energy dependence of the LDOS
is obtained from the time evolution of the local wavefunction amplitude of a
wave packet, providing a numerically efficient way to obtain information about
the multifractal exponents of the system.Comment: updated 2 references, no further change
Modeling Disordered Quantum Systems with Dynamical Networks
It is the purpose of the present article to show that so-called network
models, originally designed to describe static properties of disordered
electronic systems, can be easily generalized to quantum-{\em dynamical}
models, which then allow for an investigation of dynamical and spectral
aspects. This concept is exemplified by the Chalker-Coddington model for the
Quantum Hall effect and a three-dimensional generalization of it. We simulate
phase coherent diffusion of wave packets and consider spatial and spectral
correlations of network eigenstates as well as the distribution of
(quasi-)energy levels. Apart from that it is demonstrated how network models
can be used to determine two-point conductances. Our numerical calculations for
the three-dimensional model at the Metal-Insulator transition point delivers
among others an anomalous diffusion exponent of .
The methods presented here in detail have been used partially in earlier work.Comment: 16 pages, Rev-TeX. to appear in Int. J. Mod. Phys.
Universal Conductance and Conductivity at Critical Points in Integer Quantum Hall Systems
The sample averaged longitudinal two-terminal conductance and the respective
Kubo-conductivity are calculated at quantum critical points in the integer
quantum Hall regime. In the limit of large system size, both transport
quantities are found to be the same within numerical uncertainty in the lowest
Landau band, and , respectively. In
the 2nd lowest Landau band, a critical conductance is
obtained which indeed supports the notion of universality. However, these
numbers are significantly at variance with the hitherto commonly believed value
. We argue that this difference is due to the multifractal structure
of critical wavefunctions, a property that should generically show up in the
conductance at quantum critical points.Comment: 4 pages, 3 figure
Wave-packet dynamics at the mobility edge in two- and three-dimensional systems
We study the time evolution of wave packets at the mobility edge of
disordered non-interacting electrons in two and three spatial dimensions. The
results of numerical calculations are found to agree with the predictions of
scaling theory. In particular, we find that the -th moment of the
probability density scales like in dimensions. The
return probability scales like , with the generalized
dimension of the participation ratio . For long times and short distances
the probability density of the wave packet shows power law scaling
. The numerical calculations were performed
on network models defined by a unitary time evolution operator providing an
efficient model for the study of the wave packet dynamics.Comment: 4 pages, RevTeX, 4 figures included, published versio
Spectral Properties of the Chalker-Coddington Network
We numerically investigate the spectral statistics of pseudo-energies for the
unitary network operator U of the Chalker--Coddington network. The shape of the
level spacing distribution as well the scaling of its moments is compared to
known results for quantum Hall systems. We also discuss the influence of
multifractality on the tail of the spacing distribution.Comment: JPSJ-style, 7 pages, 4 Postscript figures, to be published in J.
Phys. Soc. Jp
Spectral Properties of Three Dimensional Layered Quantum Hall Systems
We investigate the spectral statistics of a network model for a three
dimensional layered quantum Hall system numerically. The scaling of the
quantity is used to determine the critical exponent for
several interlayer coupling strengths. Furthermore, we determine the level
spacing distribution as well as the spectral compressibility at
criticality. We show that the tail of decays as with
and also numerically verify the equation
, where is the correlation dimension and the
spatial dimension.Comment: 4 pages, 5 figures submitted to J. Phys. Soc. Jp
Localization in non-chiral network models for two-dimensional disordered wave mechanical systems
Scattering theoretical network models for general coherent wave mechanical
systems with quenched disorder are investigated. We focus on universality
classes for two dimensional systems with no preferred orientation: Systems of
spinless waves undergoing scattering events with broken or unbroken time
reversal symmetry and systems of spin 1/2 waves with time reversal symmetric
scattering. The phase diagram in the parameter space of scattering strengths is
determined. The model breaking time reversal symmetry contains the critical
point of quantum Hall systems but, like the model with unbroken time reversal
symmetry, only one attractive fixed point, namely that of strong localization.
Multifractal exponents and quasi-one-dimensional localization lengths are
calculated numerically and found to be related by conformal invariance.
Furthermore, they agree quantitatively with theoretical predictions. For
non-vanishing spin scattering strength the spin 1/2 systems show
localization-delocalization transitions.Comment: 4 pages, REVTeX, 4 figures (postscript
From quantum graphs to quantum random walks
We give a short overview over recent developments on quantum graphs and
outline the connection between general quantum graphs and so-called quantum
random walks.Comment: 14 pages, 6 figure
Universal Multifractality in Quantum Hall Systems with Long-Range Disorder Potential
We investigate numerically the localization-delocalization transition in
quantum Hall systems with long-range disorder potential with respect to
multifractal properties. Wavefunctions at the transition energy are obtained
within the framework of the generalized Chalker--Coddington network model. We
determine the critical exponent characterizing the scaling behavior
of the local order parameter for systems with potential correlation length
up to magnetic lengths . Our results show that does not
depend on the ratio . With increasing , effects due to classical
percolation only cause an increase of the microscopic length scale, whereas the
critical behavior on larger scales remains unchanged. This proves that systems
with long-range disorder belong to the same universality class as those with
short-range disorder.Comment: 4 pages, 2 figures, postsript, uuencoded, gz-compresse
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