Tunneling edges at strong disorder

Scattering between edge states that bound one-dimensional domains of opposite potential or flux is studied, in the presence of strong potential or flux disorder. A mobility edge is found as a function of disorder and energy, and we have characterized the extended phase. "paper_FINAL.tex" 439 lines, 20366 characters In the presence of flux and/or potential disorder, the localization length scales exponentially with the width of the barrier. We discuss implications for the random-flux problem.Comment: RevTeX, 4 page

Diffusion and dispersion of passive tracers: Navier-Stokes versus MHD turbulence

A comparison of turbulent diffusion and pair-dispersion in homogeneous, macroscopically isotropic Navier-Stokes (NS) and nonhelical magnetohydrodynamic (MHD) turbulence based on high-resolution direct numerical simulations is presented. Significant differences between MHD and NS systems are observed in the pair-dispersion properties, in particular a strong reduction of the separation velocity in MHD turbulence as compared to the NS case. It is shown that in MHD turbulence the average pair-dispersion is slowed down for $\tau_\mathrm{d}\lesssim t\lesssim 10 \tau_\mathrm{d}$, $\tau_\mathrm{d}$ being the Kolmogorov time, due to the alignment of the relative Lagrangian tracer velocity with the local magnetic field. Significant differences in turbulent single-particle diffusion in NS and MHD turbulence are not detected. The fluid particle trajectories in the vicinity of the smallest dissipative structures are found to be characterisically different although these comparably rare events have a negligible influence on the statistics investigated in this work.Comment: Europhysics Letters, in prin

Derivative relation for thermopower in the quantum Hall regime

Recently, Tieke et al (to be published in PRL) have observed the relation S_{yx} = alpha B dS_{xx}/dB for the components of the thermopower tensor in the quantum Hall regime, where alpha is a constant and B is the magnetic field. Simon and Halperin (PRL 73, 3278 (1994)) have suggested that an analogous relation observed for the resistivity tensor R_{xx} = \alpha B dR_{xy}/dB can be explained with a model of classical transport in an inhomogeneous medium where the local Hall resistivity is a function of position and the local dissipative resistivity is a small constant. In the present paper, we show that this new thermopower relation can be explained with a similar model.Comment: This paper supercedes cond-mat/9705001 which was withdrawn. 4 pages, Revte

Phase transition in the collisionless regime for wave-particle interaction

Gibbs statistical mechanics is derived for the Hamiltonian system coupling self-consistently a wave to N particles. This identifies Landau damping with a regime where a second order phase transition occurs. For nonequilibrium initial data with warm particles, a critical initial wave intensity is found: above it, thermodynamics predicts a finite wave amplitude in the limit of infinite N; below it, the equilibrium amplitude vanishes. Simulations support these predictions providing new insight on the long-time nonlinear fate of the wave due to Landau damping in plasmas.Comment: 12 pages (RevTeX), 2 figures (PostScript

Inviscid dynamical structures near Couette flow

Consider inviscid fluids in a channel {-1<y<1}. For the Couette flow v_0=(y,0), the vertical velocity of solutions to the linearized Euler equation at v_0 decays in time. At the nonlinear level, such inviscid damping has not been proved. First, we show that in any (vorticity) H^{s}(s<(3/2)) neighborhood of Couette flow, there exist non-parallel steady flows with arbitrary minimal horizontal period. This implies that nonlinear inviscid damping is not true in any (vorticity) H^{s}(s<(3/2)) neighborhood of Couette flow and for any horizontal period. Indeed, the long time behavior in such neighborhoods are very rich, including nontrivial steady flows, stable and unstable manifolds of nearby unstable shears. Second, in the (vorticity) H^{s}(s>(3/2)) neighborhood of Couette, we show that there exist no non-parallel steadily travelling flows v(x-ct,y), and no unstable shears. This suggests that the long time dynamics in H^{s}(s>(3/2)) neighborhoods of Couette might be much simpler. Such contrasting dynamics in H^{s} spaces with the critical power s=(3/2) is a truly nonlinear phenomena, since the linear inviscid damping near Couette is true for any initial vorticity in L^2

Evidence for topological nonequilibrium in magnetic configurations

We use direct numerical simulations to study the evolution, or relaxation, of magnetic configurations to an equilibrium state. We use the full single-fluid equations of motion for a magnetized, non-resistive, but viscous fluid; and a Lagrangian approach is used to obtain exact solutions for the magnetic field. As a result, the topology of the magnetic field remains unchanged, which makes it possible to study the case of topological nonequilibrium. We find two cases for which such nonequilibrium appears, indicating that these configurations may develop singular current sheets.Comment: 10 pages, 5 figure

Explanation for the Resistivity Law in Quantum Hall System

We consider a 2D electron system in a strong magnetic field, where the local Hall resistivity $\rho_{xy}(\vec r)$ is a function of position and $\rho_{xx}(\vec r)$ is small compared to $\rho_{xy}$. Particularly if the correlations fall off slowly with distance, or if fluctuations exist on several length scales, one finds that the macroscopic longitudinal resistivity $R_{xx}$ is only weakly dependent on $\rho_{xx}$ and is approximately proportional to the magnitude of fluctuations in $\rho_{xy}$. This may provide an explanation of the empirical law $R_{xx} \propto B \frac{dR_{xy}}{dB}$ where $R_{xy}$ is the Hall resistance, and $B$ is the magnetic field.Comment: 11 pages (REVTeX 3.0). Revised Version. Complete postscript file for this paper is available on the World Wide Web at http://cmtw.harvard.edu/~simon/ ; Preprint number HU-CMT-94S0

Statistical properties of the low-temperature conductance peak-heights for Corbino discs in the quantum Hall regime

A recent theory has provided a possible explanation for the ``non-universal scaling'' of the low-temperature conductance (and conductivity) peak-heights of two-dimensional electron systems in the integer and fractional quantum Hall regimes. This explanation is based on the hypothesis that samples which show this behavior contain density inhomogeneities. Theory then relates the non-universal conductance peak-heights to the ``number of alternating percolation clusters'' of a continuum percolation model defined on the spatially-varying local carrier density. We discuss the statistical properties of the number of alternating percolation clusters for Corbino disc samples characterized by random density fluctuations which have a correlation length small compared to the sample size. This allows a determination of the statistical properties of the low-temperature conductance peak-heights of such samples. We focus on a range of filling fraction at the center of the plateau transition for which the percolation model may be considered to be critical. We appeal to conformal invariance of critical percolation and argue that the properties of interest are directly related to the corresponding quantities calculated numerically for bond-percolation on a cylinder. Our results allow a lower bound to be placed on the non-universal conductance peak-heights, and we compare these results with recent experimental measurements.Comment: 7 pages, 4 postscript figures included. Revtex with epsf.tex and multicol.sty. The revised version contains some additional discussion of the theory and slightly improved numerical result

Propagation of Electron Magnetohydrodynamic structures in a 2-D inhomogeneous plasma

The fully three dimensional governing equations in the electron magnetohydrodynamic (EMHD) regime for a plasma with inhomogeneous density is obtained. These equations in the two dimensional (2-D) limit can be cast in terms of the evolution of two coupled scalar fields. The nonlinear simulations for the two dimensional case are carried out to understand the propagation of EMHD magnetic structures in the presence of inhomogeneity. A novel effect related to trapping of dipolar magnetic structures in the high density plasma region in the EMHD regime is observed. The interpretation of this phenomena as well as its relevance to the problem of hot spot generation in the context of fast ignition is presented

Chaotic Interaction of Langmuir Solitons and Long Wavelength Radiation

In this work we analyze the interaction of isolated solitary structures and ion-acoustic radiation. If the radiation amplitude is small solitary structures persists, but when the amplitude grows energy transfer towards small spatial scales occurs. We show that transfer is particularly fast when a fixed point of a low dimensional model is destroyed.Comment: LaTex + 4 eps file