Emergence of Functional Specificity in Balanced Networks with Synaptic Plasticity

In rodent visual cortex, synaptic connections between orientation-selective neurons are unspecific at the time of eye opening, and become to some degree functionally specific only later during development. An explanation for this two-stage process was proposed in terms of Hebbian plasticity based on visual experience that would eventually enhance connections between neurons with similar response features. For this to work, however, two conditions must be satisfied: First, orientation selective neuronal responses must exist before specific recurrent synaptic connections can be established. Second, Hebbian learning must be compatible with the recurrent network dynamics contributing to orientation selectivity, and the resulting specific connectivity must remain stable for unspecific background activity. Previous studies have mainly focused on very simple models, where the receptive fields of neurons were essentially determined by feedforward mechanisms, and where the recurrent network was small, lacking the complex recurrent dynamics of large-scale networks of excitatory and inhibitory neurons. Here we studied the emergence of functionally specific connectivity in large-scale recurrent networks with synaptic plasticity. Our results show that balanced random networks, which already exhibit highly selective responses at eye opening, can develop feature-specific connectivity if appropriate rules of synaptic plasticity are invoked within and between excitatory and inhibitory populations. If these conditions are met, the initial orientation selectivity guides the process of Hebbian learning and, as a result, functionally specific and a surplus of bidirectional connections emerge. Our results thus demonstrate the cooperation of synaptic plasticity and recurrent dynamics in large-scale functional networks with realistic receptive fields, highlight the role of inhibition as a critical element in this process, and paves the road for further computational studies of sensory processing in neocortical network models equipped with synaptic plasticity

Transport through graphene nanoribbons: suppression of transverse quantization by symmetry breaking

We investigate transport through nanoribbons in the presence of disorder scattering. We show that size quantization patterns are only present when SU(2) pseudospin symmetry is preserved. Symmetry breaking disorder renders transverse quantization invisible, which may provide an explanation for the necessity of suspending graphene nanoconstrictions to obtain size quantization signatures in very recent experiments. Employing a quasi-classical Monte-Carlo simulation, we are able to reproduce and explain key qualitative features of the full quantum-mechanical calculations.Comment: 5 figure

Phase rigidity and avoided level crossings in the complex energy plane

We consider the effective Hamiltonian of an open quantum system, its biorthogonal eigenfunctions $\phi_\lambda$ and define the value $r_\lambda = (\phi_\lambda|\phi_\lambda)/$ that characterizes the phase rigidity of the eigenfunctions $\phi_\lambda$. In the scenario with avoided level crossings, $r_\lambda$ varies between 1 and 0 due to the mutual influence of neighboring resonances. The variation of $r_\lambda$ may be considered as an internal property of an {\it open} quantum system. In the literature, the phase rigidity $\rho$ of the scattering wave function $\Psi^E_C$ is considered. Since $\Psi^E_C$ can be represented in the interior of the system by the $\phi_\lambda$, the phase rigidity $\rho$ of the $\Psi^E_C$ is related to the $r_\lambda$ and therefore also to the mutual influence of neighboring resonances. As a consequence, the reduction of the phase rigidity $\rho$ to values smaller than 1 should be considered, at least partly, as an internal property of an open quantum system in the overlapping regime. The relation to measurable values such as the transmission through a quantum dot, follows from the fact that the transmission is, in any case, resonant with respect to the effective Hamiltonian. We illustrate the relation between phase rigidity $\rho$ and transmission numerically for small open cavities.Comment: 6 pages, 3 figure

Spectroscopic properties of large open quantum-chaotic cavities with and without separated time scales

The spectroscopic properties of an open large Bunimovich cavity are studied numerically in the framework of the effective Hamiltonian formalism. The cavity is opened by attaching leads to it in four different ways. In some cases, short-lived and long-lived resonance states coexist. The short-lived states cause traveling waves in the transmission while the long-lived ones generate superposed fluctuations. The traveling waves oscillate as a function of energy. They are not localized in the interior of the large chaotic cavity. In other cases, the transmission takes place via standing waves with an intensity that closely follows the profile of the resonances. In all considered cases, the phase rigidity fluctuates with energy. It is mostly near to its maximum value and agrees well with the theoretical value for the two-channel case. As shown in the foregoing paper \cite{1}, all cases are described well by the Poisson kernel when the calculation is restricted to an energy region in which the average $S$ matrix is (nearly) constant.Comment: 13 pages, 4 figure

Whispering gallery modes in open quantum billiards

The poles of the S-matrix and the wave functions of open 2D quantum billiards with convex boundary of different shape are calculated by the method of complex scaling. Two leads are attached to the cavities. The conductance of the cavities is calculated at energies with one, two and three open channels in each lead. Bands of overlapping resonance states appear which are localized along the convex boundary of the cavities and contribute coherently to the conductance. These bands correspond to the whispering gallery modes appearing in the classical calculations.Comment: 9 pages, 3 figures in jpg and gif forma

Quantum interference from remotely trapped ions

We observe quantum interference of photons emitted by two continuously laser-excited single ions, independently trapped in distinct vacuum vessels. High contrast two-photon interference is observed in two experiments with different ion species, calcium and barium. Our experimental findings are quantitatively reproduced by Bloch equation calculations. In particular, we show that the coherence of the individual resonance fluorescence light field is determined from the observed interference