400 research outputs found
Levy Flights in Inhomogeneous Media
We investigate the impact of external periodic potentials on superdiffusive
random walks known as Levy flights and show that even strongly superdiffusive
transport is substantially affected by the external field. Unlike ordinary
random walks, Levy flights are surprisingly sensitive to the shape of the
potential while their asymptotic behavior ceases to depend on the Levy index
. Our analysis is based on a novel generalization of the Fokker-Planck
equation suitable for systems in thermal equilibrium. Thus, the results
presented are applicable to the large class of situations in which
superdiffusion is caused by topological complexity, such as diffusion on folded
polymers and scale-free networks.Comment: 4 pages, 4 figure
Anomalous diffusion as a signature of collapsing phase in two dimensional self-gravitating systems
A two dimensional self-gravitating Hamiltonian model made by
fully-coupled classical particles exhibits a transition from a collapsing phase
(CP) at low energy to a homogeneous phase (HP) at high energy. From a dynamical
point of view, the two phases are characterized by two distinct single-particle
motions : namely, superdiffusive in the CP and ballistic in the HP. Anomalous
diffusion is observed up to a time that increases linearly with .
Therefore, the finite particle number acts like a white noise source for the
system, inhibiting anomalous transport at longer times.Comment: 10 pages, Revtex - 3 Figs - Submitted to Physical Review
Quenched and Negative Hall Effect in Periodic Media: Application to Antidot Superlattices
We find the counterintuitive result that electrons move in OPPOSITE direction
to the free electron E x B - drift when subject to a two-dimensional periodic
potential. We show that this phenomenon arises from chaotic channeling
trajectories and by a subtle mechanism leads to a NEGATIVE value of the Hall
resistivity for small magnetic fields. The effect is present also in
experimentally recorded Hall curves in antidot arrays on semiconductor
heterojunctions but so far has remained unexplained.Comment: 10 pages, 4 figs on request, RevTeX3.0, Europhysics Letters, in pres
Particle Dispersion on Rapidly Folding Random Hetero-Polymers
We investigate the dynamics of a particle moving randomly along a disordered
hetero-polymer subjected to rapid conformational changes which induce
superdiffusive motion in chemical coordinates. We study the antagonistic
interplay between the enhanced diffusion and the quenched disorder. The
dispersion speed exhibits universal behavior independent of the folding
statistics. On the other hand it is strongly affected by the structure of the
disordered potential. The results may serve as a reference point for a number
of translocation phenomena observed in biological cells, such as protein
dynamics on DNA strands.Comment: 4 pages, 4 figure
A repulsive trap for two electrons in a magnetic field
We study numerically and analytically the dynamics of two classical electrons
with Coulomb interaction in a two dimensional antidot superlattice potential in
the presence of crossed electric and magnetic fields. It is found that near one
antidot the electron pair can be trapped for a long time and the escape rate
from such a trap is proportional to the square of a weak electric field. This
is qualitatively different from the case of noninteracting electrons which are
trapped forever by the antidot. For the pair propagation in the antidot
superlattice we found a broad parameter regime for which the pair is stable and
where two repulsive electrons propagate together on an enormously large
distance.Comment: revtex, 5 pages, 6 figure
What determines the spreading of a wave packet?
The multifractal dimensions D2^mu and D2^psi of the energy spectrum and
eigenfunctions, resp., are shown to determine the asymptotic scaling of the
width of a spreading wave packet. For systems where the shape of the wave
packet is preserved the k-th moment increases as t^(k*beta) with
beta=D2^mu/D2^psi, while in general t^(k*beta) is an optimal lower bound.
Furthermore, we show that in d dimensions asymptotically in time the center of
any wave packet decreases spatially as a power law with exponent D_2^psi - d
and present numerical support for these results.Comment: Physical Review Letters to appear, 4 pages postscript with figure
Statistics of resonances and of delay times in quasiperiodic Schr"odinger equations
We study the statistical distributions of the resonance widths , and of delay times in one dimensional
quasi-periodic tight-binding systems with one open channel. Both quantities are
found to decay algebraically as , and on
small and large scales respectively. The exponents , and are
related to the fractal dimension of the spectrum of the closed system
as and . Our results are verified for the
Harper model at the metal-insulator transition and for Fibonacci lattices.Comment: 4 pages, 3 figures, submitted to Phys. Rev. Let
A mechanical model of normal and anomalous diffusion
The overdamped dynamics of a charged particle driven by an uniform electric
field through a random sequence of scatterers in one dimension is investigated.
Analytic expressions of the mean velocity and of the velocity power spectrum
are presented. These show that above a threshold value of the field normal
diffusion is superimposed to ballistic motion. The diffusion constant can be
given explicitly. At the threshold field the transition between conduction and
localization is accompanied by an anomalous diffusion. Our results exemplify
that, even in the absence of time-dependent stochastic forces, a purely
mechanical model equipped with a quenched disorder can exhibit normal as well
as anomalous diffusion, the latter emerging as a critical property.Comment: 16 pages, no figure
Experimental evidence for the role of cantori as barriers in a quantum system
We investigate the effect of cantori on momentum diffusion in a quantum
system. Ultracold caesium atoms are subjected to a specifically designed
periodically pulsed standing wave. A cantorus separates two chaotic regions of
the classical phase space. Diffusion through the cantorus is classically
predicted. Quantum diffusion is only significant when the classical phase-space
area escaping through the cantorus per period greatly exceeds Planck's
constant. Experimental data and a quantum analysis confirm that the cantori act
as barriers.Comment: 19 pages including 9 figures, Accepted for publication in Physical
Review E in March 199
Bloch Electrons in a Magnetic Field - Why Does Chaos Send Electrons the Hard Way?
We find that a 2D periodic potential with different modulation amplitudes in
x- and y-direction and a perpendicular magnetic field may lead to a transition
to electron transport along the direction of stronger modulation and to
localization in the direction of weaker modulation. In the experimentally
accessible regime we relate this new quantum transport phenomenon to avoided
band crossing due to classical chaos.Comment: 4 pages, 3 figures, minor modifications, PRL to appea
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