Entropy of Horizons, Complex Paths and Quantum Tunneling

In any spacetime, it is possible to have a family of observers following a congruence of timelike curves such that they do not have access to part of the spacetime. This lack of information suggests associating a (congruence dependent) notion of entropy with the horizon that blocks the information from these observers. While the blockage of information is absolute in classical physics, quantum mechanics will allow tunneling across the horizon. This process can be analysed in a simple, yet general, manner and we show that the probability for a system with energy $E$ to tunnel across the horizon is $P(E)\propto\exp[-(2\pi/\kappa)E)$ where $\kappa$ is the surface gravity of the horizon. If the surface gravity changes due to the leakage of energy through the horizon, then one can associate an entropy $S(M)$ with the horizon where $dS = [ 2\pi / \kappa (M) ] dM$ and $M$ is the active gravitational mass of the system. Using this result, we discuss the conditions under which, a small patch of area $\Delta A$ of the horizon contributes an entropy $(\Delta A/4L_P^2)$, where $L_P^2$ is the Planck area.Comment: published versio

Understanding the radio emission geometry of PSR B0329+54

We have analyzed high-quality single pulse data of PSR B0329+54 at 325 MHz and 606 MHz to study the structure of the emission beam. Using the window-threshold technique, which is suitable for detecting weak emission components, we have detected 4 additional emission components in the pulse window. Three of these are new components and the fourth is a confirmation of a recently proposed component. Hence PSR B0329+54 is now known to have 9 emission components - the highest among all known pulsars. The distribution of the pulse components around the central core component indicates that the emission beam consists of four nested cones. The asymmetry in the location of the conal components in the leading versus trailing parts of the profile is interpreted as being due to aberration and retardation in the pulsar magnetosphere. These measurements allow us to determine the precise location of the 4 conal rings of emission. We find that the successive outer cones are emitted at higher altitudes in the magnetosphere. Further, for any given cone, the emission height at the lower frequency is found to be more than that at the higher frequency. The inferred heights range from ~160 km to ~1150 km. The set of ``active'' field lines, from which most of the conal radiation appears to originate, are found to be confined to a region located within ~0.5 to ~0.6 of the polar cap radius. We discuss the implications of our new findings on our understanding of the pulsar emission geometry and its impact on the emission mechanisms.Comment: 20 pages, 5 figures. Accepted for Astrophysical Journa

Chronological Inversion Method for the Dirac Matrix in Hybrid Monte Carlo

In Hybrid Monte Carlo simulations for full QCD, the gauge fields evolve smoothly as a function of Molecular Dynamics time. Here we investigate improved methods of estimating the trial or starting solutions for the Dirac matrix inversion as superpositions of a chronological sequence of solutions in the recent past. By taking as the trial solution the vector which minimizes the residual in the linear space spanned by the past solutions, the number of conjugate gradient iterations per unit MD time is decreased by at least a factor of 2. Extensions of this basic approach to precondition the conjugate gradient iterations are also discussed.Comment: 35 pages, 18 EPS figures A new "preconditioning" method, derived from the Chronological Inversion, is described. Some new figures are appended. Some reorganization of the material has taken plac

Non-perturbative improvement of bilinears in unquenched QCD

We describe how the improvement of quark bilinears generalizes from quenched to unquenched QCD, and discuss which of the additional improvement constants can be determined using Ward Identities.Comment: LATTICE99 (Improvement and Renormalization). 3 pages, no figures. Corrected error (improvement coefficient $g_T$ is not needed