Ginsparg-Wilson relation and the overlap formula

The fermionic determinant of a lattice Dirac operator that obeys the Ginsparg-Wilson relation factorizes into two factors that are complex conjugate of each other. Each factor is naturally associated with a single chiral fermion and can be realized as a overlap of two many body vacua.Comment: 4 pages, plain tex, no figure

Non‐Rayleigh Statistics of Ultrasonic Backscattered Echo from Tissues

The envelope of the backscattered signal from tissues can exhibit non‐Rayleigh statistics if the number density of scatterers is small or if the variations in the scattering cross sections are random. The K distribution which has been used extensively in radar, is introduced to model this non‐Rayleigh behavior. The generalized K distribution is extremely useful since it encompasses a wide range of distributions such as Rayleigh, Lognormal, and Rician. Computer simulations were conducted using a simple one‐dimensional discrete scatteringmodel to investigate the properties of the echo envelope. In addition to cases of low number densities, significant departures from Rayleigh statistics were seen as the scattering cross sections of the scatterers become random. The validity of this model was also tested using data from tissue mimicking phantoms. Results indicate that the density function of the envelope can be modeled by the K distribution and the parameters of the K distribution can provide information on the nature of the scattering region in terms of the number density of the scatterers as well as the scattering cross sections of the scatterers in the range cell. [Work was supported by NSF Grant No. BCS‐9207385.

Nonlocal effects in the shot noise of diffusive superconductor - normal-metal systems

A cross-shaped diffusive system with two superconducting and two normal electrodes is considered. A voltage $eV < \Delta$ is applied between the normal leads. Even in the absence of average current through the superconducting electrodes their presence increases the shot noise at the normal electrodes and doubles it in the case of a strong coupling to the superconductors. The nonequilibrium noise at the superconducting electrodes remains finite even in the case of a vanishingly small transport current due to the absence of energy transfer into the superconductors. This noise is suppressed by electron-electron scattering at sufficiently high voltages.Comment: 4 pages, RevTeX, 2 eps figure

Stellar Mixing and the Primordial Lithium Abundance

We compare the properties of recent samples of the lithium abundances in halo stars to one another and to the predictions of theoretical models including rotational mixing, and we examine the data for trends with metal abundance. We find from a KS test that in the absence of any correction for chemical evolution, the Ryan, Norris, & Beers (1999} sample is fully consistent with mild rotational mixing induced depletion and, therefore, with an initial lithium abundance higher than the observed value. Tests for outliers depend sensitively on the threshold for defining their presence, but we find a 10$--$45% probability that the RNB sample is drawn from the rotationally mixed models with a 0.2 dex median depletion (with lower probabilities corresponding to higher depletion factors). When chemical evolution trends (Li/H versus Fe/H) are treated in the linear plane we find that the dispersion in the RNB sample is not explained by chemical evolution; the inferred bounds on lithium depletion from rotational mixing are similar to those derived from models without chemical evolution. We find that differences in the equivalent width measurements are primarily responsible for different observational conclusions concerning the lithium dispersion in halo stars. The standard Big Bang Nucleosynthesis predicted lithium abundance which corresponds to the deuterium abundance inferred from observations of high-redshift, low-metallicity QSO absorbers requires halo star lithium depletion in an amount consistent with that from our models of rotational mixing, but inconsistent with no depletion.Comment: 39 pages, 9 figures; submitted Ap

Bounds on the Wilson Dirac Operator

New exact upper and lower bounds are derived on the spectrum of the square of the hermitian Wilson Dirac operator. It is hoped that the derivations and the results will be of help in the search for ways to reduce the cost of simulations using the overlap Dirac operator. The bounds also apply to the Wilson Dirac operator in odd dimensions and are therefore relevant to domain wall fermions as well.Comment: 16 pages, TeX, 3 eps figures, small corrections and improvement

Properties of the Fixed Point Lattice Dirac Operator in the Schwinger Model

We present a numerical study of the properties of the Fixed Point lattice Dirac operator in the Schwinger model. We verify the theoretical bounds on the spectrum, the existence of exact zero modes with definite chirality, and the Index Theorem. We show by explicit computation that it is possible to find an accurate approximation to the Fixed Point Dirac operator containing only very local couplings.Comment: 38 pages, LaTeX, 3 figures, uses style [epsfig], a few comments and relevant references adde

On the continuum limit of fermionic topological charge in lattice gauge theory

It is proved that the fermionic topological charge of SU(N) lattice gauge fields on the 4-torus, given in terms of a spectral flow of the Hermitian Wilson--Dirac operator, or equivalently, as the index of the Overlap Dirac operator, reduces to the continuum topological charge in the classical continuum limit when the parameter $m_0$ is in the physical region $0<m_0<2$.Comment: latex, 18 pages. v2: Several comments added. To appear in J.Math.Phy

Strong to weak coupling transitions of SU(N) gauge theories in 2+1 dimensions

We investigate strong-to-weak coupling transitions in D=2+1 SU(N->oo) gauge theories, by simulating lattice theories with a Wilson plaquette action. We find that there is a strong-to-weak coupling cross-over in the lattice theory that appears to become a third-order phase transition at N=oo, in a manner that is essentially identical to the Gross-Witten transition in the D=1+1 SU(oo) lattice gauge theory. There is also evidence for a second order transition at N=oo at approximately the same coupling, which is connected with centre monopoles (instantons) and so analogues to the first order bulk transition that occurs in D=3+1 lattice gauge theories for N>4. We show that as the lattice spacing is reduced, the N=oo gauge theory on a finite 3-torus suffers a sequence of (apparently) first-order ZN symmetry breaking transitions associated with each of the tori (ordered by size). We discuss how these transitions can be understood in terms of a sequence of deconfining transitions on ever-more dimensionally reduced gauge theories.We investigate whether the trace of the Wilson loop has a non-analyticity in the coupling at some critical area, but find no evidence for this although, just as in D=1+1,the eigenvalue density of a Wilson loop forms a gap at N=oo for a critical trace. The physical implications of this are unclear.The gap formation is a special case of a remarkable similarity between the eigenvalue spectra of Wilson loops in D=1+1 and D=2+1 (and indeed D=3+1): for the same value of the trace, the eigenvalue spectra are nearly identical.This holds for finite as well as infinite N; irrespective of the Wilson loop size in lattice units; and for Polyakov as well as Wilson loops.Comment: 44 pages, 28 figures. Extensive changes and clarifications with new results on non-analyticities and eigenvalue spectra of Wilson loops. This version to be submitted for publicatio

Domain-wall fermions with U(1)U(1) dynamical gauge fields

We have carried out a numerical simulation of a domain-wall model in $(2+1)$-dimensions, in the presence of a dynamical gauge field only in an extra dimension, corresponding to the weak coupling limit of a ( 2-dimensional ) physical gauge coupling. Using a quenched approximation we have investigated this model at $\beta_{s} ( = 1 / g^{2}_{s} ) =$ 0.5 ( ``symmetric'' phase), 1.0, and 5.0 (``broken'' phase), where $g_s$ is the gauge coupling constant of the extra dimension. We have found that there exists a critical value of a domain-wall mass $m_{0}^{c}$ which separates a region with a fermionic zero mode on the domain-wall from the one without it, in both symmetric and broken phases. This result suggests that the domain-wall method may work for the construction of lattice chiral gauge theories.Comment: 27 pages (11 figures), latex (epsf style-file needed