221 research outputs found
Sequential Desynchronization in Networks of Spiking Neurons with Partial Reset
The response of a neuron to synaptic input strongly depends on whether or not
it has just emitted a spike. We propose a neuron model that after spike
emission exhibits a partial response to residual input charges and study its
collective network dynamics analytically. We uncover a novel desynchronization
mechanism that causes a sequential desynchronization transition: In globally
coupled neurons an increase in the strength of the partial response induces a
sequence of bifurcations from states with large clusters of synchronously
firing neurons, through states with smaller clusters to completely asynchronous
spiking. We briefly discuss key consequences of this mechanism for more general
networks of biophysical neurons
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
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
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
Diffusion in normal and critical transient chaos
In this paper we investigate deterministic diffusion in systems which are
spatially extended in certain directions but are restricted in size and open in
other directions, consequently particles can escape. We introduce besides the
diffusion coefficient D on the chaotic repeller a coefficient which
measures the broadening of the distribution of trajectories during the
transient chaotic motion. Both coefficients are explicitly computed for
one-dimensional models, and they are found to be different in most cases. We
show furthermore that a jump develops in both of the coefficients for most of
the initial distributions when we approach the critical borderline where the
escape rate equals the Liapunov exponent of a periodic orbit.Comment: 4 pages Revtex file in twocolumn format with 2 included postscript
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
Equilibrium and dynamical properties of two dimensional self-gravitating systems
A system of N classical particles in a 2D periodic cell interacting via
long-range attractive potential is studied. For low energy density a
collapsed phase is identified, while in the high energy limit the particles are
homogeneously distributed. A phase transition from the collapsed to the
homogeneous state occurs at critical energy U_c. A theoretical analysis within
the canonical ensemble identifies such a transition as first order. But
microcanonical simulations reveal a negative specific heat regime near .
The dynamical behaviour of the system is affected by this transition : below
U_c anomalous diffusion is observed, while for U > U_c the motion of the
particles is almost ballistic. In the collapsed phase, finite -effects act
like a noise source of variance O(1/N), that restores normal diffusion on a
time scale diverging with N. As a consequence, the asymptotic diffusion
coefficient will also diverge algebraically with N and superdiffusion will be
observable at any time in the limit N \to \infty. A Lyapunov analysis reveals
that for U > U_c the maximal exponent \lambda decreases proportionally to
N^{-1/3} and vanishes in the mean-field limit. For sufficiently small energy,
in spite of a clear non ergodicity of the system, a common scaling law \lambda
\propto U^{1/2} is observed for any initial conditions.Comment: 17 pages, Revtex - 15 PS Figs - Subimitted to Physical Review E - Two
column version with included figures : less paper waste
Quantum mechanical relaxation of open quasiperiodic systems
We study the time evolution of the survival probability in open
one-dimensional quasiperiodic tight-binding samples of size , at critical
conditions. We show that it decays algebraically as up
to times , where , and
is the fractal dimension of the spectrum of the closed system. We
verified these results for the Harper model at the metal-insulator transition
and for Fibonacci lattices. Our predictions should be observable in propagation
experiments with electrons or classical waves in quasiperiodic superlattices or
dielectric multilayers.Comment: 4 pages, 5 figure
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