Dielectric function, screening, and plasmons in 2D graphene

The dynamical dielectric function of two dimensional graphene at arbitrary wave vector $q$ and frequency $\omega$, $\epsilon(q,\omega)$, is calculated in the self-consistent field approximation. The results are used to find the dispersion of the plasmon mode and the electrostatic screening of the Coulomb interaction in 2D graphene layer within the random phase approximation. At long wavelengths ($q\to 0$) the plasmon dispersion shows the local classical behavior $\omega_{cl} = \omega_0 \sqrt{q}$, but the density dependence of the plasma frequency ($\omega_0 \propto n^{1/4}$) is different from the usual 2D electron system ($\omega_0 \propto n^{1/2}$). The wave vector dependent plasmon dispersion and the static screening function show very different behavior than the usual 2D case.Comment: 6 pages, 3 figure

Response of electrically coupled spiking neurons: a cellular automaton approach

Experimental data suggest that some classes of spiking neurons in the first layers of sensory systems are electrically coupled via gap junctions or ephaptic interactions. When the electrical coupling is removed, the response function (firing rate {\it vs.} stimulus intensity) of the uncoupled neurons typically shows a decrease in dynamic range and sensitivity. In order to assess the effect of electrical coupling in the sensory periphery, we calculate the response to a Poisson stimulus of a chain of excitable neurons modeled by $n$-state Greenberg-Hastings cellular automata in two approximation levels. The single-site mean field approximation is shown to give poor results, failing to predict the absorbing state of the lattice, while the results for the pair approximation are in good agreement with computer simulations in the whole stimulus range. In particular, the dynamic range is substantially enlarged due to the propagation of excitable waves, which suggests a functional role for lateral electrical coupling. For probabilistic spike propagation the Hill exponent of the response function is $\alpha=1$, while for deterministic spike propagation we obtain $\alpha=1/2$, which is close to the experimental values of the psychophysical Stevens exponents for odor and light intensities. Our calculations are in qualitative agreement with experimental response functions of ganglion cells in the mammalian retina.Comment: 11 pages, 8 figures, to appear in the Phys. Rev.