Dephasing in matter-wave interferometry

We review different attempts to show the decoherence process in double-slit-like experiments both for charged particles (electrons) and neutral particles with permanent dipole moments. Interference is studied when electrons or atomic systems are coupled to classical or quantum electromagnetic fields. The interaction between the particles and time-dependent fields induces a time-varying Aharonov phase. Averaging over the phase generates a suppression of fringe visibility in the interference pattern. We show that, for suitable experimental conditions, the loss of contrast for dipoles can be almost as large as the corresponding one for coherent electrons and therefore, be observed. We analyze different trajectories in order to show the dependence of the decoherence factor with the velocity of the particles.Comment: 9 pages, 1 eps-figure. To appear in J. Phys. A: Math. Ge

Symmetric hyperbolic system in the Ashtekar formulation

We present a first-order symmetric hyperbolic system in the Ashtekar formulation of general relativity for vacuum spacetime. We add terms from constraint equations to the evolution equations with appropriate combinations, which is the same technique used by Iriondo, Leguizam\'on and Reula [Phys. Rev. Lett. 79, 4732 (1997)]. However our system is different from theirs in the points that we primarily use Hermiticity of a characteristic matrix of the system to characterize our system "symmetric", discuss the consistency of this system with reality condition, and show the characteristic speeds of the system.Comment: 4 pages, RevTeX, to appear in Phys. Rev. Lett., Comments added, refs update

Illustrating Stability Properties of Numerical Relativity in Electrodynamics

We show that a reformulation of the ADM equations in general relativity, which has dramatically improved the stability properties of numerical implementations, has a direct analogue in classical electrodynamics. We numerically integrate both the original and the revised versions of Maxwell's equations, and show that their distinct numerical behavior reflects the properties found in linearized general relativity. Our results shed further light on the stability properties of general relativity, illustrate them in a very transparent context, and may provide a useful framework for further improvement of numerical schemes.Comment: 5 pages, 2 figures, to be published as Brief Report in Physical Review

Constraints and Reality Conditions in the Ashtekar Formulation of General Relativity

We show how to treat the constraints and reality conditions in the $SO(3)$-ADM (Ashtekar) formulation of general relativity, for the case of a vacuum spacetime with a cosmological constant. We clarify the difference between the reality conditions on the metric and on the triad. Assuming the triad reality condition, we find a new variable, allowing us to solve the gauge constraint equations and the reality conditions simultaneously.Comment: LaTeX file, 12 pages, no figures; to appear in Classical and Quantum Gravit

Schwarzschild Tests of the Wahlquist-Estabrook-Buchman-Bardeen Tetrad Formulation for Numerical Relativity

A first order symmetric hyperbolic tetrad formulation of the Einstein equations developed by Estabrook and Wahlquist and put into a form suitable for numerical relativity by Buchman and Bardeen (the WEBB formulation) is adapted to explicit spherical symmetry and tested for accuracy and stability in the evolution of spherically symmetric black holes (the Schwarzschild geometry). The lapse and shift which specify the evolution of the coordinates relative to the tetrad congruence are reset at frequent time intervals to keep the constant-time hypersurfaces nearly orthogonal to the tetrad congruence and the spatial coordinate satisfying a kind of minimal rate of strain condition. By arranging through initial conditions that the constant-time hypersurfaces are asymptotically hyperbolic, we simplify the boundary value problem and improve stability of the evolution. Results are obtained for both tetrad gauges (``Nester'' and ``Lorentz'') of the WEBB formalism using finite difference numerical methods. We are able to obtain stable unconstrained evolution with the Nester gauge for certain initial conditions, but not with the Lorentz gauge.Comment: (accepted by Phys. Rev. D) minor changes; typos correcte

A trick for passing degenerate points in Ashtekar formulation

We examine one of the advantages of Ashtekar's formulation of general relativity: a tractability of degenerate points from the point of view of following the dynamics of classical spacetime. Assuming that all dynamical variables are finite, we conclude that an essential trick for such a continuous evolution is in complexifying variables. In order to restrict the complex region locally, we propose some `reality recovering' conditions on spacetime. Using a degenerate solution derived by pull-back technique, and integrating the dynamical equations numerically, we show that this idea works in an actual dynamical problem. We also discuss some features of these applications.Comment: 9 pages by RevTeX or 16 pages by LaTeX, 3 eps figures and epsf-style file are include

Extending the lifetime of 3D black hole computations with a new hyperbolic system of evolution equations

We present a new many-parameter family of hyperbolic representations of Einstein's equations, which we obtain by a straightforward generalization of previously known systems. We solve the resulting evolution equations numerically for a Schwarzschild black hole in three spatial dimensions, and find that the stability of the simulation is strongly dependent on the form of the equations (i.e. the choice of parameters of the hyperbolic system), independent of the numerics. For an appropriate range of parameters we can evolve a single 3D black hole to $t \simeq 600 M$ -- $1300 M$, and are apparently limited by constraint-violating solutions of the evolution equations. We expect that our method should result in comparable times for evolutions of a binary black hole system.Comment: 11 pages, 2 figures, submitted to PR

Long term stable integration of a maximally sliced Schwarzschild black hole using a smooth lattice method

We will present results of a numerical integration of a maximally sliced Schwarzschild black hole using a smooth lattice method. The results show no signs of any instability forming during the evolutions to t=1000m. The principle features of our method are i) the use of a lattice to record the geometry, ii) the use of local Riemann normal coordinates to apply the 1+1 ADM equations to the lattice and iii) the use of the Bianchi identities to assist in the computation of the curvatures. No other special techniques are used. The evolution is unconstrained and the ADM equations are used in their standard form.Comment: 47 pages including 26 figures, plain TeX, also available at http://www.maths.monash.edu.au/~leo/preprint

Efficient Set Sharing Using ZBDDs

Set sharing is an abstract domain in which each concrete object is represented by the set of local variables from which it might be reachable. It is a useful abstraction to detect parallelism opportunities, since it contains definite information about which variables do not share in memory, i.e., about when the memory regions reachable from those variables are disjoint. Set sharing is a more precise alternative to pair sharing, in which each domain element is a set of all pairs of local variables from which a common object may be reachable. However, the exponential complexity of some set sharing operations has limited its wider application. This work introduces an efficient implementation of the set sharing domain using Zero-suppressed Binary Decision Diagrams (ZBDDs). Because ZBDDs were designed to represent sets of combinations (i.e., sets of sets), they naturally represent elements of the set sharing domain. We show how to synthesize the operations needed in the set sharing transfer functions from basic ZBDD operations. For some of the operations, we devise custom ZBDD algorithms that perform better in practice. We also compare our implementation of the abstract domain with an efficient, compact, bit set-based alternative, and show that the ZBDD version scales better in terms of both memory usage and running time