Anderson localization of a Tonks-Girardeau gas in potentials with controlled disorder

We theoretically demonstrate features of Anderson localization in the Tonks-Girardeau gas confined in one-dimensional (1D) potentials with controlled disorder. That is, we investigate the evolution of the single particle density and correlations of a Tonks-Girardeau wave packet in such disordered potentials. The wave packet is initially trapped, the trap is suddenly turned off, and after some time the system evolves into a localized steady state due to Anderson localization. The density tails of the steady state decay exponentially, while the coherence in these tails increases. The latter phenomenon corresponds to the same effect found in incoherent optical solitons

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

Pattern Competition in the Photorefractive Semiconductors

We analytically study the photorefractive Gunn effect in n-GaAs subjected to two external laser beams which form a moving interference pattern (MIP) in the semiconductor. When the intensity of the spatially independent part of the MIP, denoted by $I_0$, is small, the system has a periodic domain train (PDT), consistent with the results of linear stability analysis. When $I_0$ is large, the space-charge field induced by the MIP will compete with the PDT and result in complex dynamics, including driven chaos via quasiperiodic route

On the Photorefractive Gunn Effect

We present and numerically solve a model of the photorefractive Gunn effect. We find that high field domains can be triggered by phase-locked interference fringes, as it has been recently predicted on the basis of linear stability considerations. Since the Gunn effect is intrinsically nonlinear, we find that such considerations give at best order-of-magnitude estimations of the parameters critical to the photorefractive Gunn effect. The response of the system is much more complex including multiple wave shedding from the injecting contact, wave suppression and chaos with spatial structure.Comment: Revtex, 8 pag., 4 fig. (jpg), submit to Physical Review

Visible Array Waveguide Gratings for Applications of Optical Neural Probes

In this paper we propose using Array Waveguide Gratings (AWGs), working in the visible range, in order to implement the technique of Wavelength-Division-(de)Multiplexing for multi-point stimulation of deep-brain neurons. We've developed a CMOS compatible fabrication process and fabricated two sets of AWGs, working in the red and blue wavelengths. Experimental data demonstrating the functionality of these AWGs is presented

An Analytical Approach to Neuronal Connectivity

This paper describes how realistic neuromorphic networks can have their connectivity properties fully characterized in analytical fashion. By assuming that all neurons have the same shape and are regularly distributed along the two-dimensional orthogonal lattice with parameter $\Delta$, it is possible to obtain the accurate number of connections and cycles of any length from the autoconvolution function as well as from the respective spectral density derived from the adjacency matrix. It is shown that neuronal shape plays an important role in defining the spatial spread of network connections. In addition, most such networks are characterized by the interesting phenomenon where the connections are progressively shifted along the spatial domain where the network is embedded. It is also shown that the number of cycles follows a power law with their respective length. Morphological measurements for characterization of the spatial distribution of connections, including the adjacency matrix spectral density and the lacunarity of the connections, are suggested. The potential of the proposed approach is illustrated with respect to digital images of real neuronal cells.Comment: 4 pages, 6 figure

Induced Coherence and Stable Soliton Spiraling

We develop a theory of soliton spiraling in a bulk nonlinear medium and reveal a new physical mechanism: periodic power exchange via induced coherence, which can lead to stable spiraling and the formation of dynamical two-soliton states. Our theory not only explains earlier observations, but provides a number of predictions which are also verified experimentally. Finally, we show theoretically and experimentally that soliton spiraling can be controled by the degree of mutual initial coherence.Comment: 4 pages, 5 figure