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

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

Anomalous diffusion as a signature of collapsing phase in two dimensional self-gravitating systems

A two dimensional self-gravitating Hamiltonian model made by $N$ 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 $\tau$ that increases linearly with $N$. 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

Evolutionary optimization of an experimental apparatus

In recent decades, cold atom experiments have become increasingly complex. While computers control most parameters, optimization is mostly done manually. This is a time-consuming task for a high-dimensional parameter space with unknown correlations. Here we automate this process using a genetic algorithm based on Differential Evolution. We demonstrate that this algorithm optimizes 21 correlated parameters and that it is robust against local maxima and experimental noise. The algorithm is flexible and easy to implement. Thus, the presented scheme can be applied to a wide range of experimental optimization tasks.Comment: minor revisio

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

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 ${\hat D}$ 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 ${\cal P} (\Gamma)$, and of delay times ${\cal P} (\tau)$ in one dimensional quasi-periodic tight-binding systems with one open channel. Both quantities are found to decay algebraically as $\Gamma^{-\alpha}$, and $\tau^{-\gamma}$ on small and large scales respectively. The exponents $\alpha$, and $\gamma$ are related to the fractal dimension $D_0^E$ of the spectrum of the closed system as $\alpha=1+D_0^E$ and $\gamma=2-D_0^E$. 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 $U$ 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 $U_c$. 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 $N$-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

The possibility of a metal insulator transition in antidot arrays induced by an external driving

It is shown that a family of models associated with the kicked Harper model is relevant for cyclotron resonance experiments in an antidot array. For this purpose a simplified model for electronic motion in a related model system in presence of a magnetic field and an AC electric field is developed. In the limit of strong magnetic field it reduces to a model similar to the kicked Harper model. This model is studied numerically and is found to be extremely sensitive to the strength of the electric field. In particular, as the strength of the electric field is varied a metal -- insulator transition may be found. The experimental conditions required for this transition are discussed.Comment: 6 files: kharp.tex, fig1.ps fig2.ps fi3.ps fig4.ps fig5.p