Modeling of Spiking-Bursting Neural Behavior Using Two-Dimensional Map

A simple model that replicates the dynamics of spiking and spiking-bursting activity of real biological neurons is proposed. The model is a two-dimensional map which contains one fast and one slow variable. The mechanisms behind generation of spikes, bursts of spikes, and restructuring of the map behavior are explained using phase portrait analysis. The dynamics of two coupled maps which model the behavior of two electrically coupled neurons is discussed. Synchronization regimes for spiking and bursting activity of these maps are studied as a function of coupling strength. It is demonstrated that the results of this model are in agreement with the synchronization of chaotic spiking-bursting behavior experimentally found in real biological neurons.Comment: 9 pages, 12 figure

Infrared luminosities of galaxies in the Local Volume

Near-infrared properties of 451 galaxies with distances D \leq 10 Mpc are considered basing on the all-sky two micron survey (2MASS). A luminosity function of the galaxies in the K-band is derived within [-25,-11] mag. The local (D < 8 Mpc) luminosity density is estimated to be 6.8*10^8 L_sun/Mpc^3 that exceeds (1.5+-0.1) times the global cosmic density in the K-band. Virial mass-to-K-luminosity ratios are determined for nearby groups and clusters. In the luminosity range of (5*10^{10} - 2*10^{13})L_sun, the groups and clusters follow the relation \lg(M/L_K) propto (0.27+-0.03) lg(L_K) with a scatter of \~0.1 comparable to errors of the observables. The mean ratio ~= (20-25) M_sun/L_sun for the galaxy systems turns out to be significantly lower than the global ratio, (80-90)M_sun/L_sun, expected in the standard cosmological model with the matter density of Omega_m =0.27. This discrepancy can be resolved if most of dark matter in the universe is not associated with galaxies and their systems.Comment: 15 pages, 7 figures. Astronomy Letters, submitte

Weak levitation of 2D delocalized states in a magnetic field.

The deviation of the energy position of a delocalized state from the center of Landau level is studied in the framework of the Chalker-Coddington model. It is demonstrated that introducing a weak Landau level mixing results in a shift of the delocalized state up in energy. The mechanism of a levitation is a neighboring - Landau level - assisted resonant tunneling which ``shunts'' the saddle-points. The magnitude of levitation is shown to be independent of the Landau level number.Comment: Latex file (12 pages) + 3 Postscript figures

Planck Scale Physics of the Single Particle Schr\"{o}dinger Equation with Gravitational Self-Interaction

We consider the modification of a single particle Schr\"{o}dinger equation by the inclusion of an additional gravitational self-potential term which follows from the prescription that the' mass-density'that enters this term is given by $m |\psi (\vec {r},t)|^2$, where $\psi (\vec {r}, t)$ is the wavefunction and $m$ is the mass of the particle. This leads to a nonlinear equation, the ' Newton Schrodinger' equation, which has been found to possess stationary self-bound solutions, whose energy can be determined exactly using an asymptotic method. We find that such a particle strongly violates superposition and becomes a black hole as its mass approaches the Planck mass.Comment: 16 pages, Revtex, No figure, Submitted to Physics Letters

A Fermi Fluid Description of the Half-Filled Landau Level

We present a many-body approach to calculate the ground state properties of a system of electrons in a half-filled Landau level. Our starting point is a simplified version of the recently proposed trial wave function where one includes the antisymmetrization operator to the bosonic Laughlin state. Using the classical plasma analogy, we calculate the pair-correlation function, the static structure function and the ground state energy in the thermodynamic limit. These results are in good agreement with the expected behavior at $\nu=\frac12$.Comment: 4 pages, REVTEX, and 4 .ps file

Deconfinement transition in three-dimensional compact U(1) gauge theories coupled to matter fields

It is shown that permanent confinement in three-dimensional compact U(1) gauge theory can be destroyed by matter fields in a deconfinement transition. This is a consequence of a non-trivial infrared fixed point caused by matter, and an anomalous scaling dimension of the gauge field. This leads to a logarithmic interaction between the defects of the gauge-fields, which form a gas of magnetic monopoles. In the presence of logarithmic interactions, the original electric charges are unconfined. The confined phase which is permanent in the absence of matter fields is reached at a critical electric charge, where the interaction between magnetic charges is screened by a pair unbinding transition in a Kosterlitz-Thouless type of phase-transition.Comment: RevTex4, 4 pages, no figures; version accepted for publication in PR

Rotational cooling of heteronuclear molecular ions with ^1-Sigma, ^2-Sigma, ^3-Sigma and ^2-Pi electronic ground states

The translational motion of molecular ions can be effectively cooled sympathetically to translational temperatures below 100 mK in ion traps through Coulomb interactions with laser-cooled atomic ions. The ro-vibrational degrees of freedom, however, are expected to be largely unaffected during translational cooling. We have previously proposed schemes for cooling of the internal degrees of freedom of such translationally cold but internally hot heteronuclear diatomic ions in the simplest case of ^1-Sigma electronic ground state molecules. Here we present a significant simplification of these schemes and make a generalization to the most frequently encountered electronic ground states of heteronuclear molecular ions: ^1-Sigma, ^2-Sigma, ^3-Sigma and ^2-Pi. The schemes are relying on one or two laser driven transitions with the possible inclusion of a tailored incoherent far infrared radiation field.Comment: 16 pages, 13 figure

Melting of the classical bilayer Wigner crystal: influence of the lattice symmetry

The melting transition of the five different lattices of a bilayer crystal is studied using the Monte-Carlo technique. We found the surprising result that the square lattice has a substantial larger melting temperature as compared to the other lattice structures, which is a consequence of the specific topology of the temperature induced defects. A new melting criterion is formulated which we show to be universal for bilayers as well as for single layer crystals.Comment: 4 pages, 5 figures (postscript files). Accepted in Physical Review Letter

Collapse of Spin-Splitting in the Quantum Hall Effect

It is known experimentally that at not very large filling factors $\nu$ the quantum Hall conductivity peaks corresponding to the same Landau level number $N$ and two different spin orientations are well separated. These peaks occur at half-integer filling factors $\nu = 2 N + 1/2$ and $\nu = 2 N + 3/2$ so that the distance between them $\delta\nu$ is unity. As $\nu$ increases $\delta\nu$ shrinks. Near certain $N = N_c$ two peaks abruptly merge into a single peak at $\nu = 2N + 1$. We argue that this collapse of the spin-splitting at low magnetic fields is attributed to the disorder-induced destruction of the exchange enhancement of the electron $g$-factor. We use the mean-field approach to show that in the limit of zero Zeeman energy $\delta\nu$ experiences a second-order phase transition as a function of the magnetic field. We give explicit expressions for $N_c$ in terms of a sample's parameters. For example, we predict that for high-mobility heterostructures $N_c = 0.9 d n^{5/6} n_i^{-1/3},$ where $d$ is the spacer width, $n$ is the density of the two-dimensional electron gas, and $n_i$ is the two-dimensional density of randomly situated remote donors.Comment: 14 pages, compressed Postscript fil

A Survey of Merger Remnants II: The Emerging Kinematic and Photometric Correlations

This paper is the second in a series exploring the properties of 51 {\it optically} selected, single-nuclei merger remnants. Spectroscopic data have been obtained for a sub-sample of 38 mergers and combined with previously obtained infrared photometry to test whether mergers exhibit the same correlations as elliptical galaxies among parameters such as stellar luminosity and distribution, central stellar velocity dispersion ($\sigma$$_{\circ}$), and metallicity. Paramount to the study is to test whether mergers lie on the Fundamental Plane. Measurements of $\sigma$$_{\circ}$ have been made using the Ca triplet absorption line at 8500 {\AA} for all 38 mergers in the sub-sample. Additional measurements of $\sigma$$_{\circ}$ were made for two of the mergers in the sub-sample using the CO absorption line at 2.29 \micron. The results indicate that mergers show a strong correlation among the parameters of the Fundamental Plane but fail to show a strong correlation between $\sigma$$_{\circ}$ and metallicity (Mg$_{2}$). In contrast to earlier studies, the $\sigma$$_{\circ}$ of the mergers are consistent with objects which lie somewhere between intermediate-mass and luminous giant elliptical galaxies. However, the discrepancies with earlier studies appears to correlate with whether the Ca triplet or CO absorption lines are used to derive $\sigma$$_{\circ}$, with the latter almost always producing smaller values. Finally, the photometric and kinematic data are used to demonstrate for the first time that the central phase-space density of mergers are equivalent to elliptical galaxies. This resolves a long-standing criticism of the merger hypothesis.Comment: Accepted Astronomical Journal (to appear in January 2006