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 $N= 200 \times 200$ 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

Transport properties near the Anderson transition

The electronic transport properties in the presence of a temperature gradient in disordered systems near the metal-insulator transition [MIT] are considered. The d.c. conductivity $\sigma$, the thermoelectric power $S$, the thermal conductivity $K$ and the Lorenz number $L_0$ are calculated for the three-dimensional Anderson model of localization using the Chester-Thellung-Kubo-Greenwood formulation of linear response. We show that $\sigma$, S, K and $L_0$ can be scaled to one-parameter scaling curves with a single scaling paramter $k_BT/|{\mu-E_c}/E_c|$.Comment: 4 pages, 4 EPS figures, uses annalen.cls style [included]; presented at Localization 1999, to appear in Annalen der Physik [supplement

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, $\lambda_{2}$, for two interacting particles (TIP) in a one-dimensional random potential, presenting its dependence on disorder, interaction strength $U$ and system size. $\lambda_{2}(U)$ is computed by a decimation method from the decay of the Green function along the diagonal of finite samples. Infinite sample size estimates $\xi_{2}(U)$ 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 $U$, we find that $\xi_{2}(U) \sim \xi_2(0)^{\beta(U)}$ with $\beta(U)$ varying between $\beta(0)=1$ and $\beta(1) \approx 1.5$. 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