arXiv subjects

Theo Geisel

Publications and source records attributed to Theo Geisel.

33 records · Page 2Linked to original sources

arXiv2004

Signatures of Classical Diffusion in Quantum Fluctuations of 2D Chaotic Systems

We consider a two-dimensional (2D) generalization of the standard kicked-rotor (KR) and show that it is an excellent model for the study of 2D quantum systems with underlying diffusive classical dynamics. First we analyze the distribution of wavefunction intensities and compare them with the predictions derived in the framework of diffusive {\it disordered} samples. Next, we turn the closed system into an open one by constructing a scattering matrix. The distribution of the resonance widths ${\cal P}(Γ)$ and Wigner delay times ${\cal P}(τ_W)$ are investigated. The forms of these distributions are obtained for different symmetry classes and the traces of classical diffusive dynamics are identified. Our theoretical arguments are supported by extensive numerical calculations.

cond-mat.mes-hall↗

arXiv2004

Long Chaotic Transients in Complex Networks

We show that long chaotic transients dominate the dynamics of randomly diluted networks of pulse-coupled oscillators. This contrasts with the rapid convergence towards limit cycle attractors found in networks of globally coupled units. The lengths of the transients strongly depend on the network connectivity and varies by several orders of magnitude, with maximum transient lengths at intermediate connectivities. The dynamics of the transient exhibits a novel form of robust synchronization. An approximation to the largest Lyapunov exponent characterizing the chaotic nature of the transient dynamics is calculated analytically.

cond-mat.dis-nn↗

arXiv2003

The Intrinsic Time Scale of Transient Neuronal Responses

In a generic neuron model, we present the linear response theory for the firing rate in response to both time dependent input currents and noise amplitudes. In both cases the signal transmission is strongly attenuated for frequencies above the stationary firing rate. For high frequencies both the mean input and the noise transmission function decay as ω^{-2}, independent of model details. Our results indicate that previously suggested mechanisms for near instantaneous transmission of information are not consistent with the spike generation mechanism of real neurons.

physics.bio-ph↗

arXiv2003

Quantum Reversibility: Is there an Echo?

We study the possibility to undo the quantum mechanical evolution in a time reversal experiment. The naive expectation, as reflected in the common terminology ("Loschmidt echo"), is that maximum compensation results if the reversed dynamics extends to the same time as the forward evolution. We challenge this belief, and demonstrate that the time $t_r$ for maximum return probability is in general shorter. We find that $t_r$ depends on $lambda = eps_evol/eps_prep$, being the ratio of the error in setting the parameters (fields) for the time reversed evolution to the perturbation which is involved in the preparation process. Our results should be observable in spin-echo experiments where the dynamical irreversibility of quantum phases is measured.

quant-ph↗

arXiv2003

Breaking Synchrony by Heterogeneity in Complex Networks

For networks of pulse-coupled oscillators with complex connectivity, we demonstrate that in the presence of coupling heterogeneity precisely timed periodic firing patterns replace the state of global synchrony that exists in homogenous networks only. With increasing disorder, these patterns persist until they reach a critical temporal extent that is of the order of the interaction delay. For stronger disorder these patterns cease to exist and only asynchronous, aperiodic states are observed. We derive self-consistency equations to predict the precise temporal structure of a pattern from the network heterogeneity. Moreover, we show how to design heterogenous coupling architectures to create an arbitrary prescribed pattern.

cond-mat.dis-nn↗

arXiv2003

Topological Speed Limits to Network Synchronization

We study collective synchronization of pulse-coupled oscillators interacting on asymmetric random networks. We demonstrate that random matrix theory can be used to accurately predict the speed of synchronization in such networks in dependence on the dynamical and network parameters. Furthermore, we show that the speed of synchronization is limited by the network connectivity and stays finite, even if the coupling strength becomes infinite. In addition, our results indicate that synchrony is robust under structural perturbations of the network dynamics.

cond-mat.dis-nn↗

arXiv2003

Shot noise from action correlations

We consider universal shot noise in ballistic chaotic cavities from a semiclassical point of view and show that it is due to action correlations within certain groups of classical trajectories. Using quantum graphs as a model system we sum these trajectories analytically and find agreement with random-matrix theory. Unlike all action correlations which have been considered before, the correlations relevant for shot noise involve four trajectories and do not depend on the presence of any symmetry.

cond-mat.mes-hall↗

arXiv2003

Coexistence of regular and irregular dynamics in complex networks of pulse-coupled oscillators

For general networks of pulse-coupled oscillators, including regular, random, and more complex networks, we develop an exact stability analysis of synchronous states. As opposed to conventional stability analysis, here stability is determined by a multitude of linear operators. We treat this multi-operator problem analytically and show that for inhibitory interactions the synchronous state is stable, independent of the parameters and the network connectivity. In randomly connected networks with strong interactions this synchronous state, displaying \textit{regular} dynamics, coexists with a balanced state that exhibits \textit{irregular} dynamics such that external signals may switch the network between qualitatively distinct states.

cond-mat.dis-nn↗

arXiv2002

Prevalence of unstable attractors in networks of pulse-coupled oscillators

We present and analyze the first example of a dynamical system that naturally exhibits attracting periodic orbits that are \textit{unstable}. These unstable attractors occur in networks of pulse-coupled oscillators where they prevail for large networks and a wide range of parameters. They are enclosed by basins of attraction of other attractors but are remote from their own basin volume such that arbitrarily small noise leads to a switching among attractors.

cond-mat.dis-nn↗

arXiv2002

Unstable attractors induce perpetual synchronization and desynchronization

Common experience suggests that attracting invariant sets in nonlinear dynamical systems are generally stable. Contrary to this intuition, we present a dynamical system, a network of pulse-coupled oscillators, in which \textit{unstable attractors} arise naturally. From random initial conditions, groups of synchronized oscillators (clusters) are formed that send pulses alternately, resulting in a periodic dynamics of the network. Under the influence of arbitrarily weak noise, this synchronization is followed by a desynchronization of clusters, a phenomenon induced by attractors that are unstable. Perpetual synchronization and desynchronization lead to a switching among attractors. This is explained by the geometrical fact, that these unstable attractors are surrounded by basins of attraction of other attractors, whereas the full measure of their own basin is located remote from the attractor. Unstable attractors do not only exist in these systems, but moreover dominate the dynamics for large networks and a wide range of parameters.

cond-mat.dis-nn↗

arXiv2001

Stochastic Resonance in Neuron Models: Endogenous Stimulation Revisited

The paradigm of stochastic resonance (SR)---the idea that signal detection and transmission may benefit from noise---has met with great interest in both physics and the neurosciences. We investigate here the consequences of reducing the dynamics of a periodically driven neuron to a renewal process (stimulation with reset or endogenous stimulation). This greatly simplifies the mathematical analysis, but we show that stochastic resonance as reported earlier occurs in this model only as a consequence of the reduced dynamics.

physics.bio-ph↗

arXiv2000

Spreading and localization of wavepackets in disordered wires in a magnetic field

We study the diffusive and localization properties of wavepackets in disordered wires in a magnetic field. In contrast to a recent supersymmetry approach our numerical results show that the decay rate of the steady state changes {\em smoothly} at the crossover from preserved to broken time-reversal symmetry. Scaling and fluctuation properties are also analyzed and a formula, which was derived analytically only in the pure symmetry cases is shown to describe also the steady state wavefunction at the crossover regime. Finally, we present a scaling for the variance of the packet which shows again a smooth transition due to the magnetic field.

cond-mat.mes-hall↗

arXiv2000

Scaling properties of one-dimensional Anderson models in an electric field: Exponential vs. factorial localization

We investigate the scaling properties of eigenstates of a one-dimensional (1D) Anderson model in the presence of a constant electric field. The states show a transition from exponential to factorial localization. For infinite systems this transition can be described by a simple scaling law based on a single parameter $λ_{\infty} = l_{\infty}/l_{\rm el}$, the ratio between the Anderson localization length $l_{\infty}$ and the Stark localization length~$l_{\rm el}$. For finite samples, however, the system size $N$ enters the problem as a third parameter. In that case the global structure of eigenstates is uniquely determined by two scaling parameters $λ_N=l_\infty/N$ and $λ_\infty=l_\infty/l_{\rm el}$.

cond-mat.dis-nn↗

arXiv2000

Signal Selection Based on Stochastic Resonance

Noise aids the encoding of continuous signals into pulse sequences by way of stochastic resonance and endows the encoding device with a preferred frequency. We study encoding by a threshold device based on the Ornstein-Uhlenbeck process, equivalent to the leaky integrate-and-fire neuron model. Preferred frequency, optimum noise intensity, and optimum signal-to-noise ratio are shown to be linearly related to the AC amplitude of the input signal. The DC component of the input tunes the device either into transmission (preferred frequency nearly independent of signal amplitude) or selection mode (frequency rising with amplitude). We argue that this behavior may facilitate selective signal processing in neurons.

physics.bio-ph↗

arXiv1998

Markov analysis of stochastic resonance in a periodically driven integrate-fire neuron

We model the dynamics of the leaky integrate-fire neuron under periodic stimulation as a Markov process with respect to the stimulus phase. This avoids the unrealistic assumption of a stimulus reset after each spike made in earlier work and thus solves the long-standing reset problem. The neuron exhibits stochastic resonance, both with respect to input noise intensity and stimulus frequency. The latter resonance arises by matching the stimulus frequency to the refractory time of the neuron. The Markov approach can be generalized to other periodically driven stochastic processes containing a reset mechanism.

physics.bio-ph↗