865 research outputs found
Numerical investigations of scaling at the Anderson transition
At low temperature T, a significant difference between the behavior of
crystals on the one hand and disordered solids on the other is seen:
sufficiently strong disorder can give rise to a transition of the transport
properties from conducting behavior with finite resistance R to insulating
behavior with R=infinity as T -> 0. This well-studied phenomenon is called the
disorder-driven metal-insulator transition and it is characteristic to
non-crystalline solids. In this review of recent advances, we have presented
results of transport studies in disordered systems, ranging from modifications
of the standard Anderson model of localization to effects of a two-body
interaction. Of paramount importance in these studies was always the highest
possible accuracy of the raw data combined with the careful subsequent
application of the finite-size scaling technique. In fact, it is this scaling
method that has allowed numerical studies to move beyond simple extrapolations
and reliably construct estimates of quantities as if one were studying an
infinite system.Comment: 18 pages, 6 figures, "The Anderson Transition and its
Ramifications-Localisation, Quantum Interference, and Interactions", 'Lecture
Notes in Physics' series, ed. T. Brandes and S. Kettemann, Springer Verlag,
to be publishe
Interaction-dependent enhancement of the localisation length for two interacting particles in a one-dimensional random potential
We present calculations of the localisation length, , for two
interacting particles (TIP) in a one-dimensional random potential, presenting
its dependence on disorder, interaction strength and system size.
is computed by a decimation method from the decay of the Green
function along the diagonal of finite samples. Infinite sample size estimates
are obtained by finite-size scaling. For U=0 we reproduce
approximately the well-known dependence of the one-particle localisation length
on disorder while for finite , we find that with varying between and
. We test the validity of various other proposed fit
functions and also study the problem of TIP in two different random potentials
corresponding to interacting electron-hole pairs. As a check of our method and
data, we also reproduce well-known results for the two-dimensional Anderson
model without interaction.Comment: 34 RevTeX 3.0 pages with 16 figures include
The two-dimensional Anderson model of localization with random hopping
We examine the localization properties of the 2D Anderson Hamiltonian with
off-diagonal disorder. Investigating the behavior of the participation numbers
of eigenstates as well as studying their multifractal properties, we find
states in the center of the band which show critical behavior up to the system
size considered. This result is confirmed by an independent
analysis of the localization lengths in quasi-1D strips with the help of the
transfer-matrix method. Adding a very small additional onsite potential
disorder, the critical states become localized.Comment: 26 RevTeX 3.0 pages with 13 figures included via psfi
Time domain modal identification/estimation of the mini-mast testbed
The Mini-Mast is a 20 meter long 3-dimensional, deployable/retractable truss structure designed to imitate future trusses in space. Presented here are results from a robust (with respect to measurement noise sensitivity), time domain, modal identification technique for identifying the modal properties of the Mini-Mast structure even in the face of noisy environments. Three testing/analysis procedures are considered: sinusoidal excitation near resonant frequencies of the Mini-Mast, frequency response function averaging of several modal tests, and random input excitation with a free response period
Two interacting particles at the metal-insulator transition
To investigate the influence of electronic interaction on the metal-insulator
transition (MIT), we consider the Aubry-Andr\'{e} (or Harper) model which
describes a quasiperiodic one-dimensional quantum system of non-interacting
electrons and exhibits an MIT. For a two-particle system, we study the effect
of a Hubbard interaction on the transition by means of the transfer-matrix
method and finite-size scaling. In agreement with previous studies we find that
the interaction localizes some states in the otherwise metallic phase of the
system. Nevertheless, the MIT remains unaffected by the interaction. For a
long-range interaction, many more states become localized for sufficiently
large interaction strength and the MIT appears to shift towards smaller
quasiperiodic potential strength.Comment: 26 RevTeX 3.0 pages with 10 EPS-figures include
Energy Levels of Quasiperiodic Hamiltonians, Spectral Unfolding, and Random Matrix Theory
We consider a tight-binding Hamiltonian defined on the quasiperiodic
Ammann-Beenker tiling. Although the density of states (DOS) is rather spiky,
the integrated DOS is quite smooth and can be used to perform spectral
unfolding. The effect of unfolding on the integrated level-spacing distribution
is investigated for various parts of the spectrum which show different
behaviour of the DOS. For energy intervals with approximately constant DOS, we
find good agreement with the distribution of the Gaussian orthogonal random
matrix ensemble (GOE) even without unfolding. For energy ranges with
fluctuating DOS, we observe deviations from the GOE result. After unfolding, we
always recover the GOE distribution.Comment: 6 pages, 4 figures, to appear in Comp. Phys. Commu
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