SU(N) Coherent States

We generalize Schwinger boson representation of SU(2) algebra to SU(N) and define coherent states of SU(N) using $2(2^{N-1}-1)$ bosonic harmonic oscillator creation and annihilation operators. We give an explicit construction of all (N-1) Casimirs of SU(N) in terms of these creation and annihilation operators. The SU(N) coherent states belonging to any irreducible representations of SU(N) are labelled by the eigenvalues of the Casimir operators and are characterized by (N-1) complex orthonormal vectors describing the SU(N) manifold. The coherent states provide a resolution of identity, satisfy the continuity property, and possess a variety of group theoretic properties.Comment: 25 pages, LaTex, no figure

Computing motion in the primate's visual system

Computing motion on the basis of the time-varying image intensity is a difficult problem for both artificial and biological vision systems. We will show how one well-known gradient-based computer algorithm for estimating visual motion can be implemented within the primate's visual system. This relaxation algorithm computes the optical flow field by minimizing a variational functional of a form commonly encountered in early vision, and is performed in two steps. In the first stage, local motion is computed, while in the second stage spatial integration occurs. Neurons in the second stage represent the optical flow field via a population-coding scheme, such that the vector sum of all neurons at each location codes for the direction and magnitude of the velocity at that location. The resulting network maps onto the magnocellular pathway of the primate visual system, in particular onto cells in the primary visual cortex (V1) as well as onto cells in the middle temporal area (MT). Our algorithm mimics a number of psychophysical phenomena and illusions (perception of coherent plaids, motion capture, motion coherence) as well as electrophysiological recordings. Thus, a single unifying principle ‘the final optical flow should be as smooth as possible’ (except at isolated motion discontinuities) explains a large number of phenomena and links single-cell behavior with perception and computational theory

Computing optical flow in the primate visual system

Computing motion on the basis of the time-varying image intensity is a difficult problem for both artificial and biological vision systems. We show how gradient models, a well-known class of motion algorithms, can be implemented within the magnocellular pathway of the primate's visual system. Our cooperative algorithm computes optical flow in two steps. In the first stage, assumed to be located in primary visual cortex, local motion is measured while spatial integration occurs in the second stage, assumed to be located in the middle temporal area (MT). The final optical flow is extracted in this second stage using population coding, such that the velocity is represented by the vector sum of neurons coding for motion in different directions. Our theory, relating the single-cell to the perceptual level, accounts for a number of psychophysical and electrophysiological observations and illusions

Short-wavelength secondary instabilities in homogeneous and stably stratified shear flows

We present a numerical investigation of three-dimensional, short-wavelength linear instabilities in Kelvin-Helmholtz (KH) vortices in homogeneous and stratified environments. The base flow, generated using two-dimensional numerical simulations, is characterized by the Reynolds number and the Richardson number defined based on the initial one-dimensional velocity and buoyancy profiles. The local stability equations are then solved on closed streamlines in the vortical base flow, which is assumed quasi-steady. For the unstratified case, the elliptic instability at the vortex core dominates at early times, before being taken over by the hyperbolic instability at the vortex edge. For the stratified case, the early time instabilities comprise a dominant elliptic instability at the core and a hyperbolic instability strongly influenced by stratification at the vortex edge. At intermediate times, the local approach shows a new branch of instability (convective branch) that emerges at the vortex core and subsequently moves towards the vortex edge. A few more convective instability branches appear at the vortex core and move away, before coalescing to form the most unstable region inside the vortex periphery at large times. The dominant instability characteristics from the local approach are shown to be in good qualitative agreement with results from global instability studies for both homogeneous and stratified cases. Compartmentalized analyses are then used to elucidate the role of shear and stratification on the identified instabilities. The role of buoyancy is shown to be critical after the primary KH instability saturates, with the dominant convective instability shown to occur in regions with the strongest statically unstable layering. We conclude by highlighting the potentially insightful role that the local approach may offer in understanding the secondary instabilities in other flows.Comment: Submitted to J. Fluid Mech., 20 pages, 10 figure

SU(N) Irreducible Schwinger Bosons

We construct SU(N) irreducible Schwinger bosons satisfying certain U(N-1) constraints which implement the symmetries of SU(N) Young tableaues. As a result all SU(N) irreducible representations are simple monomials of $(N-1)$ types of SU(N) irreducible Schwinger bosons. Further, we show that these representations are free of multiplicity problems. Thus all SU(N) representations are made as simple as SU(2).Comment: 27 pages, 5 figures, revtex

The Composite Spectrum of Strong Lyman-alpha Forest Absorbers

We present a new method for probing the physical conditions and metal enrichment of the Intergalactic Medium: the composite spectrum of Ly-alpha forest absorbers. We apply this technique to a sample of 9480 Ly-alpha absorbers with redshift 2 < z < 3.5 identified in the spectra of 13,279 high-redshift quasars from the Sloan Digital Sky Survey (SDSS) Fifth Data Release (DR5). Absorbers are selected as local minima in the spectra with 2.4 < tau_Ly-alpha < 4.0; at SDSS resolution (~ 150km/s FWHM), these absorbers are blends of systems that are individually weaker. In the stacked spectra we detect seven Lyman-series lines and metal lines of O VI, N V, C IV, C III, Si IV, C II, Al II, Si II, Fe II, Mg II, and O I. Many of these lines have peak optical depths of < 0.02, but they are nonetheless detected at high statistical significance. Modeling the Lyman-series measurements implies that our selected systems have total H I column densities N_HI ~ 10^15.4cm-2. Assuming typical physical conditions rho / = 10, T = 10^4 - 10^4.5 K, and [Fe/H]= -2 yields reasonable agreement with the line strengths of high-ionization species, but it underpredicts the low-ionization species by two orders of magnitude or more. This discrepancy suggests that the low ionization lines arise in dense, cool, metal-rich clumps, present in some absorption systems.Comment: 7 pages, 4 figures, 1 table, accepted by ApJL, revisions mad