388 research outputs found
Microscopic details of stripes and bubbles in the quantum Hall regime
We use a fully self-consistent laterally resolved Hartree-Fock approximation for numerically addressing the electron configurations at higher Landau levels in the quantum Hall regime for nearmacroscopic sample sizes. At low disorder we find, spatially-resolved, stripe- and bubble-like charge density modulations and show how these emerge depending on the filling factor. The microscopic details of these boundary regions determine the geometrical boundary conditions for aligning the charge density modulation either as stripes or bubbles. Transport is modelled using a non-equilibrium network model giving a pronounced anisotropy in direction of the injected current in the stripe regime close to half filling. We obtain a stripe period of 2.9 cyclotron radii. Our results provide an intuitive understanding of its consequences in strong magnetic fields and indicate the dominance of many particle physics in the integer quantum Hall regime when studied at legnth scales
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
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
Two-peak soliton in the CKP hierarchy
We present a systematic approach to the construction of soliton solutions for the 5-reduction of the C-type sub-hierarchy for the Kadomtsev–Petviashvili (CKP) hierarchies starting from the general τ-function τ(n+k) of the Kadomtsev–Petviashvili (KP) hierarchy. We obtain the one-soliton and two-soliton solutions for the bi-directional Kaup–Kupershmidt (bKK) equation, i.e. the 5-reduction of CKP hierarchy
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
Multifractal analysis with the probability density function at the three-dimensional Anderson transition
The probability density function (PDF) for critical wavefunction amplitudes
is studied in the three-dimensional Anderson model. We present a formal
expression between the PDF and the multifractal spectrum f(alpha) in which the
role of finite-size corrections is properly analyzed. We show the non-gaussian
nature and the existence of a symmetry relation in the PDF. From the PDF, we
extract information about f(alpha) at criticality such as the presence of
negative fractal dimensions and we comment on the possible existence of
termination points. A PDF-based multifractal analysis is hence shown to be a
valid alternative to the standard approach based on the scaling of general
inverse participation ratios.Comment: 4 pages, 7 figure
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
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