An augmented moment method for stochastic ensembles with delayed couplings: II. FitzHugh-Nagumo model

Dynamics of FitzHugh-Nagumo (FN) neuron ensembles with time-delayed couplings subject to white noises, has been studied by using both direct simulations and a semi-analytical augmented moment method (AMM) which has been proposed in a recent paper [H. Hasegawa, E-print: cond-mat/0311021]. For $N$-unit FN neuron ensembles, AMM transforms original $2N$-dimensional {\it stochastic} delay differential equations (SDDEs) to infinite-dimensional {\it deterministic} DEs for means and correlation functions of local and global variables. Infinite-order recursive DEs are terminated at the finite level $m$ in the level-$m$ AMM (AMM$m$), yielding $8(m+1)$-dimensional deterministic DEs. When a single spike is applied, the oscillation may be induced if parameters of coupling strength, delay, noise intensity and/or ensemble size are appropriate. Effects of these parameters on the emergence of the oscillation and on the synchronization in FN neuron ensembles have been studied. The synchronization shows the {\it fluctuation-induced} enhancement at the transition between non-oscillating and oscillating states. Results calculated by AMM5 are in fairly good agreement with those obtained by direct simulations.Comment: 15 pages, 3 figures; changed the title with correcting typos, accepted in Phys. Rev. E with some change

Regularization, Renormalization and Range: The Nucleon-Nucleon Interaction from Effective Field Theory

Regularization and renormalization is discussed in the context of low-energy effective field theory treatments of two or more heavy particles (such as nucleons). It is desirable to regulate the contact interactions from the outset by treating them as having a finite range. The low energy physical observables should be insensitive to this range provided that the range is of a similar or greater scale than that of the interaction. Alternative schemes, such as dimensional regularization, lead to paradoxical conclusions such as the impossibility of repulsive interactions for truly low energy effective theories where all of the exchange particles are integrated out. This difficulty arises because a nonrelativistic field theory with repulsive contact interactions is trivial in the sense that the $S$ matrix is unity and the renormalized coupling constant zero. Possible consequences of low energy attraction are also discussed. It is argued that in the case of large or small scattering lengths, the region of validity of effective field theory expansion is much larger if the contact interactions are given a finite range from the beginning.Comment: 7 page

Influences of an impurity on the transport properties of one-dimensional antisymmetric spin filter

The influences of an impurity on the spin and the charge transport of one-dimensional antisymmetric spin filter are investigated using bosonization and Keldysh formulation and the results are highlighted against those of spinful Luttinger liquids. Due to the dependence of the electron spin orientation on wave number the spin transport is not affected by the impurity, while the charge transport is essentially identical with that of spinless one-dimensional Luttinger liquid.Comment: 7 pages, 2 figures. To appear in Physical Review

Deformed Algebras from Inverse Schwinger Method

We consider a problem which may be viewed as an inverse one to the Schwinger realization of Lie algebra, and suggest a procedure of deforming the so-obtained algebra. We illustrate the method through a few simple examples extending Schwinger's $su(1,1)$ construction. As results, various q-deformed algebras are (re-)produced as well as their undeformed counterparts. Some extensions of the method are pointed out briefly.Comment: 14 pages, Jeonju University Report, Late

Generating Function for Particle-Number Probability Distribution in Directed Percolation

We derive a generic expression for the generating function (GF) of the particle-number probability distribution (PNPD) for a simple reaction diffusion model that belongs to the directed percolation universality class. Starting with a single particle on a lattice, we show that the GF of the PNPD can be written as an infinite series of cumulants taken at zero momentum. This series can be summed up into a complete form at the level of a mean-field approximation. Using the renormalization group techniques, we determine logarithmic corrections for the GF at the upper critical dimension. We also find the critical scaling form for the PNPD and check its universality numerically in one dimension. The critical scaling function is found to be universal up to two non-universal metric factors.Comment: (v1,2) 8 pages, 5 figures; one-loop calculation corrected in response to criticism received from Hans-Karl Janssen, (v3) content as publishe

Discovery of GeV Emission from the Circinus galaxy with the Fermi-LAT

We report the discovery of gamma-ray emission from the Circinus galaxy using the Large Area Telescope (LAT) onboard the Fermi Gamma-ray Space Telescope. Circinus is a nearby (~4 Mpc) starburst with a heavily obscured Seyfert-type active nucleus, bipolar radio lobes perpendicular to the spiral disk, and kpc-scale jet-like structures. Our analysis of 0.1-100 GeV events collected during 4 years of LAT observations reveals a significant (~ 7.3 sigma) excess above the background. We find no indications of variability or spatial extension beyond the LAT point-spread function. A power-law model used to describe the 0.1-100 GeV gamma-ray spectrum yields a flux of (18.8+/-5.8)x10^{-9} ph cm^{-2} s^{-1} and photon index 2.19+/-0.12, corresponding to an isotropic gamma-ray luminosity of 3 x 10^{40} erg s^{-1}. This observed gamma-ray luminosity exceeds the luminosity expected from cosmic-ray interactions in the interstellar medium and inverse Compton radiation from the radio lobes. Thus the origin of the GeV excess requires further investigation.Comment: 7 pages, 7 figures, accepted for publication in the Astrophysical Journa