Operator improvement for Ginsparg-Wilson fermions

The improvement of fermionic operators for Ginsparg-Wilson fermions is investigated. We present explicit formulae for improved Green's functions, which apply both on-shell and off-shell.Comment: 13 pages, Latex, 4 postscript figure

Quenched chiral logarithms in lattice QCD with exact chiral symmetry

We examine quenched chiral logarithms in lattice QCD with overlap Dirac quark. For 100 gauge configurations generated with the Wilson gauge action at $\beta = 5.8$ on the $8^3 \times 24$ lattice, we compute quenched quark propagators for 12 bare quark masses. The pion decay constant is extracted from the pion propagator, and from which the lattice spacing is determined to be 0.147 fm. The presence of quenched chiral logarithm in the pion mass is confirmed, and its coefficient is determined to be $\delta = 0.203 \pm 0.014$, in agreement with the theoretical estimate in quenched chiral perturbation theory. Further, we obtain the topological susceptibility of these 100 gauge configurations by measuring the index of the overlap Dirac operator. Using a formula due to exact chiral symmetry, we obtain the $\eta'$ mass in quenched chiral perturbation theory, $m_{\eta'} = (901 \pm 64)$ Mev, and an estimate of $\delta = 0.197 \pm 0.027$, which is in good agreement with that determined from the pion mass.Comment: 24 pages, 6 EPS figures; v2: some clarifications added, to appear in Physical Review

The NASA/GSFC hydrogen maser program: A review of recent data

Data is presented on the phase and frequency stability, over time periods extending to one week, of the new NR field operable hydrogen masers developed by the Applied Physics Laboratory (APL) and the older NX and NP field operable hydrogen masers developed by Goddard Space Flight Center and maintained and upgraded by Bendix Field Engineering Corporation (BFEC). Data is presented on the NR masers in the laboratory showing frequency stabilities well into the 10 to the -15th power range and phase stabilities well into the 100 ps range for periods of up to one day. Data is presented on upgraded NP masers in the laboratory showing that the frequency stability has been improved substantially to virtually the NR level. VLBI data is presented on the phase difference between NX-2 at Owens Valley, California and NR-2 at Fort Davis, Texas for a one week period showing, after removal of a constant frequency drift, a 350 ps RMS phase stability

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

A Quantum Anti-Zeno Paradox

We establish an exact differential equation for the operator describing time-dependent measurements continuous in time and obtain a series solution. Suppose the projection operator $E(t) = U(t) E U^\dagger(t)$ is measured continuously from t = 0 to T, where E is a projector leaving the initial state unchanged and U(t) a unitary operator obeying U(0) = 1 and some smoothness conditions in t. We prove that the probability of always finding E(t) = 1 from t = 0 to T is unity. If $U(t) \neq 1$, the watched kettle is sure to `boil'.Comment: 10 pages,late

Factorial Moments of Continuous Order

The normalized factorial moments $F_q$ are continued to noninteger values of the order $q$, satisfying the condition that the statistical fluctuations remain filtered out. That is, for Poisson distribution $F_q = 1$ for all $q$. The continuation procedure is designed with phenomenology and data analysis in mind. Examples are given to show how $F_q$ can be obtained for positive and negative values of $q$. With $q$ being continuous, multifractal analysis is made possible for multiplicity distributions that arise from self-similar dynamics. A step-by-step procedure of the method is summarized in the conclusion.Comment: 15 pages + 9 figures (figures available upon request), Late

Experimental procedures for precision measurements of the Casimir force with an Atomic Force Microscope

Experimental methods and procedures required for precision measurements of the Casimir force are presented. In particular, the best practices for obtaining stable cantilevers, calibration of the cantilever, correction of thermal and mechanical drift, measuring the contact separation, sphere radius and the roughness are discussed.Comment: 14 pages, 7 figure

Characterizing the radiative effect of rain using a global ensemble of cloud resolving simulations

The effect of rain on radiative fluxes and heating rates is a process that is neglected in most of the large scale atmospheric models used for weather forecasting or climate prediction. Yet, to our knowledge, the magnitude of the resulting radiative bias remains unquantified. This study aims to quantify the rain radiative effect (RRE) at a range of temporal and spatial scales, as a step towards determining whether the radiation schemes in these models should include rain. Using offline radiative transfer calculations with input from an ensemble of cloud resolving model simulations, we find that rain has a negligible effect on global mean radiative fluxes (less than 0.2 W m‐2). Weekly mean RREs at specific locations may be larger (less than 4 W m−2). At the finest temporal and spatial resolutions, the RRE can occasionally be much larger again (greater than 100 W m‐2), but values exceeding 10 W m‐2 occur in less than 0.1% of cases. Using detailed analysis of case studies we demonstrate that the magnitude and direction of the RRE depend on the rain water path, its vertical location with respect to cloud and, for longwave radiation, the temperature at which it occurs. Large RREs generally only occur when the rain water path is large and the cloud water path is small. These cases are infrequent and intermittent. As the RREs are generally small, we conclude that this missing process is unlikely to be important for large scale atmospheric models