102 research outputs found
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
, 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thermopower relation can be explained with a similar model.Comment: This paper supercedes cond-mat/9705001 which was withdrawn. 4 pages,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 is a function of position and
is small compared to . Particularly if the
correlations fall off slowly with distance, or if fluctuations exist on several
length scales, one finds that the macroscopic longitudinal resistivity
is only weakly dependent on and is approximately proportional to
the magnitude of fluctuations in . This may provide an explanation
of the empirical law where is
the Hall resistance, and 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
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