The Exact Ground State of the Frenkel-Kontorova Model with Repeated Parabolic Potential: II. Numerical Treatment

A procedure is described for efficiently finding the ground state energy and configuration for a Frenkel-Kontorova model in a periodic potential, consisting of N parabolic segments of identical curvature in each period, through a numerical solution of the convex minimization problem described in the preceding paper. The key elements are the use of subdifferentials to describe the structure of the minimization problem; an intuitive picture of how to solve it, based on motion of quasiparticles; and a fast linear optimization method with a reduced memory requirement. The procedure has been tested for N up to 200.Comment: 9 RevTeX pages, using AMS-Fonts (amssym.tex,amssym.def), 3 Postscript figures, accepted by Phys.Rev.B to be published together with cond-mat/970722

Optimal Eavesdropping in Quantum Cryptography. II. Quantum Circuit

It is shown that the optimum strategy of the eavesdropper, as described in the preceding paper, can be expressed in terms of a quantum circuit in a way which makes it obvious why certain parameters take on particular values, and why obtaining information in one basis gives rise to noise in the conjugate basis.Comment: 7 pages, 1 figure, Latex, the second part of quant-ph/970103

Constraints on the distance to SGR 1806-20 from HI absorption

The giant flare detected from the magnetar SGR 1806-20 on 2004 December 27 had a fluence more than 100 times higher than the only two other SGR flares ever recorded. Whereas the fluence is independent of distance, an estimate for the luminosity of the burst depends on the source's distance, which has previously been argued to be ~15 kpc. The burst produced a bright radio afterglow, against which Cameron et al. (2005) have measured an HI absorption spectrum. This has been used to propose a revised distance to SGR 1806-20 of between 6.4 and 9.8 kpc. Here we analyze this absorption spectrum, and compare it both to HI emission data from the Southern Galactic Plane Survey and to archival 12-CO survey data. We confirm ~6 kpc, as a likely lower limit on the distance to SGR 1806-20, but argue that it is difficult to place an upper limit on the distance to SGR 1806-20 from the HI data currently available. The previous value of ~15 kpc thus remains the best estimate of the distance to the source.Comment: 3 pages, 1 embedded EPS figure. Added sentences to end of Abstract and Conclusion, clarifying that most likely distance is 15 kpc. ApJ Letters, in pres

A physical distinction between a covariant and non covariant reduction process in relativistic quantum theories

Causality imposes strong restrictions on the type of operators that may be observables in relativistic quantum theories. In fact, causal violations arise when computing conditional probabilities for certain partial causally connected measurements using the standard non covariant procedure. Here we introduce another way of computing conditional probabilities, based on an intrinsic covariant relational order of the events, which differs from the standard one when these type of measurements are included. This alternative procedure is compatible with a wider and very natural class of operators without breaking causality. If some of these measurements could be implemented in practice as predicted by our formalism, the non covariant, conventional approach should be abandoned. Furthermore, the description we promote here would imply a new physical effect where interference terms are suppressed as a consequence of the covariant order in the measurement process.Comment: 7 pages, latex file, 1 ps figure. Major presentation changes. To appear in New Journal of Physic

Classical Dynamics of the Quantum Harmonic Chain

The origin of classical predictability is investigated for the one dimensional harmonic chain considered as a closed quantum mechanical system. By comparing the properties of a family of coarse-grained descriptions of the chain, we conclude that local coarse-grainings in this family are more useful for prediction than nonlocal ones. A quantum mechanical system exhibits classical behavior when the probability is high for histories having the correlations in time implied by classical deterministic laws. But approximate classical determinism holds only for certain coarse-grainings and then only if the initial state of the system is suitably restricted. Coarse-grainings by the values of the hydrodynamic variables (integrals over suitable volumes of densities of approximately conserved quantities) define the histories usually used in classical physics. But what distinguishes this coarse-graining from others? This paper approaches this question by analyzing a family of coarse-grainings for the linear harmonic chain. At one extreme in the family the chain is divided into local groups of $N$ atoms. At the other extreme the $N$ atoms are distributed nonlocally over the whole chain. Each coarse-graining follows the average (center of mass) positions of the groups and ignores the ``internal'' coordinates within each group, these constituting a different environment for each coarse-graining. We conclude that noise, decoherence, and computational complexity favor locality over nonlocality for deterministic predictability.Comment: 38 pages RevTeX 3.0 + 4 figures (postscript). Numerous minor corrections. Submitted to Physical Review

Impulsive spherical gravitational waves

Penrose's identification with warp provides the general framework for constructing the continuous form of impulsive gravitational wave metrics. We present the 2-component spinor formalism for the derivation of the full family of impulsive spherical gravitational wave metrics which brings out the power in identification with warp and leads to the simplest derivation of exact solutions. These solutions of the Einstein vacuum field equations are obtained by cutting Minkowski space into two pieces along a null cone and re-identifying them with warp which is given by an arbitrary non-linear holomorphic transformation. Using 2-component spinor techniques we construct a new metric describing an impulsive spherical gravitational wave where the vertex of the null cone lies on a world-line with constant acceleration

Ultra-fine beryllium powder by amalgam process Progress report, period ending 31 Oct. 1966

Metallurgical evaluation of beryllium powdered metal, and electron microscope studies of agglomerate particle size

The Einstein static universe with torsion and the sign problem of the cosmological constant

In the field equations of Einstein-Cartan theory with cosmological constant a static spherically symmetric perfect fluid with spin density satisfying the Weyssenhoff restriction is considered. This serves as a rough model of space filled with (fermionic) dark matter. From this the Einstein static universe with constant torsion is constructed, generalising the Einstein Cosmos to Einstein-Cartan theory. The interplay between torsion and the cosmological constant is discussed. A possible way out of the cosmological constant's sign problem is suggested.Comment: 8 pages, LaTeX; minor layout changes, typos corrected, one new equation, new reference [5], completed reference [13], two references adde

Two qubit copying machine for economical quantum eavesdropping

We study the mapping which occurs when a single qubit in an arbitrary state interacts with another qubit in a given, fixed state resulting in some unitary transformation on the two qubit system which, in effect, makes two copies of the first qubit. The general problem of the quality of the resulting copies is discussed using a special representation, a generalization of the usual Schmidt decomposition, of an arbitrary two-dimensional subspace of a tensor product of two 2-dimensional Hilbert spaces. We exhibit quantum circuits which can reproduce the results of any two qubit copying machine of this type. A simple stochastic generalization (using a ``classical'' random signal) of the copying machine is also considered. These copying machines provide simple embodiments of previously proposed optimal eavesdropping schemes for the BB84 and B92 quantum cryptography protocols.Comment: Minor changes. 26 pages RevTex including 7 PS figure

The VLA Galactic Plane Survey

The VLA Galactic Plane Survey (VGPS) is a survey of HI and 21-cm continuum emission in the Galactic plane between longitude 18 degrees 67 degr. with latitude coverage from |b| < 1.3 degr. to |b| < 2.3 degr. The survey area was observed with the Very Large Array (VLA) in 990 pointings. Short-spacing information for the HI line emission was obtained by additional observations with the Green Bank Telescope (GBT). HI spectral line images are presented with a resolution of 1 arcmin x 1 arcmin x 1.56 km/s (FWHM) and rms noise of 2 K per 0.824 km/s channel. Continuum images made from channels without HI line emission have 1 arcmin (FWHM) resolution. VGPS images are compared with images from the Canadian Galactic Plane Survey (CGPS) and the Southern Galactic Plane Survey (SGPS). In general, the agreement between these surveys is impressive, considering the differences in instrumentation and image processing techniques used for each survey. The differences between VGPS and CGPS images are small, < 6 K (rms) in channels where the mean HI brightness temperature in the field exceeds 80 K. A similar degree of consistency is found between the VGPS and SGPS. The agreement we find between arcminute resolution surveys of the Galactic plane is a crucial step towards combining these surveys into a single uniform dataset which covers 90% of the Galactic disk: the International Galactic Plane Survey (IGPS). The VGPS data will be made available on the World Wide Web through the Canadian Astronomy Data Centre (CADC).Comment: Accepted for publication in The Astronomical Journal. 41 pages, 13 figures. For information on data release, colour images etc. see http://www.ras.ucalgary.ca/VGP