10,053 research outputs found
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
NonâRayleigh Statistics of Ultrasonic Backscattered Echo from Tissues
The envelope of the backscattered signal from tissues can exhibit nonâRayleigh 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 nonâRayleigh 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 oneâdimensional 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. BCSâ9207385.
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 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
1045% 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 is in the physical region .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 dynamical gauge fields
We have carried out a numerical simulation of a domain-wall model in
-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 0.5 ( ``symmetric'' phase),
1.0, and 5.0 (``broken'' phase), where is the gauge coupling constant of
the extra dimension. We have found that there exists a critical value of a
domain-wall mass 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
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