640 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
Complexity in parametric Bose-Hubbard Hamiltonians and structural analysis of eigenstates
We consider a family of chaotic Bose-Hubbard Hamiltonians (BHH) parameterized
by the coupling strength between neighboring sites. As increases the
eigenstates undergo changes, reflected in the structure of the Local Density of
States. We analyze these changes, both numerically and analytically, using
perturbative and semiclassical methods. Although our focus is on the quantum
trimer, the presented methodology is applicable for the analysis of longer
lattices as well.Comment: 4 pages, 4 figure
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
Speed of synchronization in complex networks of neural oscillators Analytic results based on Random Matrix Theory
We analyze the dynamics of networks of spiking neural oscillators. First, we
present an exact linear stability theory of the synchronous state for networks
of arbitrary connectivity. For general neuron rise functions, stability is
determined by multiple operators, for which standard analysis is not suitable.
We describe a general non-standard solution to the multi-operator problem.
Subsequently, we derive a class of rise functions for which all stability
operators become degenerate and standard eigenvalue analysis becomes a suitable
tool. Interestingly, this class is found to consist of networks of leaky
integrate and fire neurons. For random networks of inhibitory
integrate-and-fire neurons, we then develop an analytical approach, based on
the theory of random matrices, to precisely determine the eigenvalue
distribution. This yields the asymptotic relaxation time for perturbations to
the synchronous state which provides the characteristic time scale on which
neurons can coordinate their activity in such networks. For networks with
finite in-degree, i.e. finite number of presynaptic inputs per neuron, we find
a speed limit to coordinating spiking activity: Even with arbitrarily strong
interaction strengths neurons cannot synchronize faster than at a certain
maximal speed determined by the typical in-degree.Comment: 17 pages, 12 figures, submitted to Chao
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
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
Metal-insulator transitions in cyclotron resonance of periodic nanostructures due to avoided band crossings
A recently found metal-insulator transition in a model for cyclotron
resonance in a two-dimensional periodic potential is investigated by means of
spectral properties of the time evolution operator. The previously found
dynamical signatures of the transition are explained in terms of avoided band
crossings due to the change of the external electric field. The occurrence of a
cross-like transport is predicted and numerically confirmed
Scaling detection in time series: diffusion entropy analysis
The methods currently used to determine the scaling exponent of a complex
dynamic process described by a time series are based on the numerical
evaluation of variance. This means that all of them can be safely applied only
to the case where ordinary statistical properties hold true even if strange
kinetics are involved. We illustrate a method of statistical analysis based on
the Shannon entropy of the diffusion process generated by the time series,
called Diffusion Entropy Analysis (DEA). We adopt artificial Gauss and L\'{e}vy
time series, as prototypes of ordinary and anomalus statistics, respectively,
and we analyse them with the DEA and four ordinary methods of analysis, some of
which are very popular. We show that the DEA determines the correct scaling
exponent even when the statistical properties, as well as the dynamic
properties, are anomalous. The other four methods produce correct results in
the Gauss case but fail to detect the correct scaling in the case of L\'{e}vy
statistics.Comment: 21 pages,10 figures, 1 tabl
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