RCS043938-2904.9: A New Rich Cluster of Galaxies at z=0.951

We present deep I, J_s, K_s imaging and optical spectroscopy of the newly discovered Red-Sequence Cluster Survey cluster RCS043938-2904.9. This cluster, drawn from an extensive preliminary list, was selected for detailed study on the basis of its apparent optical richness. Spectroscopy of 11 members places the cluster at z=0.951 +- 0.006, and confirms the photometric redshift estimate from the (R-z) color-magnitude diagram. Analysis of the infrared imaging data demonstrates that the cluster is extremely rich, with excess counts in the Ks-band exceeding the expected background counts by 9 sigma. The properties of the galaxies in RCS043938-2904.9 are consistent with those seen in other clusters at similar redshifts. Specifically, the red-sequence color, slope and scatter, and the size-magnitude relation of these galaxies are all consistent with that seen in the few other high redshift clusters known, and indeed are consistent with appropriately evolved properties of local cluster galaxies. The apparent consistency of these systems implies that the rich, high-redshift RCS clusters are directly comparable to the few other systems known at z ~ 1, most of which have been selected on the basis of X-ray emission.Comment: 12 pages, 1 color figure. Accepted for publication on The ApJ Letter

Universal geometric approach to uncertainty, entropy and information

It is shown that for any ensemble, whether classical or quantum, continuous or discrete, there is only one measure of the "volume" of the ensemble that is compatible with several basic geometric postulates. This volume measure is thus a preferred and universal choice for characterising the inherent spread, dispersion, localisation, etc, of the ensemble. Remarkably, this unique "ensemble volume" is a simple function of the ensemble entropy, and hence provides a new geometric characterisation of the latter quantity. Applications include unified, volume-based derivations of the Holevo and Shannon bounds in quantum and classical information theory; a precise geometric interpretation of thermodynamic entropy for equilibrium ensembles; a geometric derivation of semi-classical uncertainty relations; a new means for defining classical and quantum localization for arbitrary evolution processes; a geometric interpretation of relative entropy; and a new proposed definition for the spot-size of an optical beam. Advantages of the ensemble volume over other measures of localization (root-mean-square deviation, Renyi entropies, and inverse participation ratio) are discussed.Comment: Latex, 38 pages + 2 figures; p(\alpha)->1/|T| in Eq. (72) [Eq. (A10) of published version

Return times, recurrence densities and entropy for actions of some discrete amenable groups

Results of Wyner and Ziv and of Ornstein and Weiss show that if one observes the first k outputs of a finite-valued ergodic process, then the waiting time until this block appears again is almost surely asymptotic to $2^{hk}$, where $h$ is the entropy of the process. We examine this phenomenon when the allowed return times are restricted to some subset of times, and generalize the results to processes parameterized by other discrete amenable groups. We also obtain a uniform density version of the waiting time results: For a process on $s$ symbols, within a given realization, the density of the initial $k$-block within larger $n$-blocks approaches $2^{-hk}$, uniformly in $n>s^k$, as $k$ tends to infinity. Again, similar results hold for processes with other indexing groups.Comment: To appear in Journal d'Analyse Mathematiqu

Monotonicity of quantum ground state energies: Bosonic atoms and stars

The N-dependence of the non-relativistic bosonic ground state energy is studied for quantum N-body systems with either Coulomb or Newton interactions. The Coulomb systems are "bosonic atoms," with their nucleus fixed, and the Newton systems are "bosonic stars". In either case there exists some third order polynomial in N such that the ratio of the ground state energy to the respective polynomial grows monotonically in N. Some applications of these new monotonicity results are discussed

The Hartree limit of Born's ensemble for the ground state of a bosonic atom or ion

The non-relativistic bosonic ground state is studied for quantum N-body systems with Coulomb interactions, modeling atoms or ions made of N "bosonic point electrons" bound to an atomic point nucleus of Z "electron" charges, treated in Born--Oppenheimer approximation. It is shown that the (negative) ground state energy E(Z,N) yields the monotonically growing function (E(l N,N) over N cubed). By adapting an argument of Hogreve, it is shown that its limit as N to infinity for l > l* is governed by Hartree theory, with the rescaled bosonic ground state wave function factoring into an infinite product of identical one-body wave functions determined by the Hartree equation. The proof resembles the construction of the thermodynamic mean-field limit of the classical ensembles with thermodynamically unstable interactions, except that here the ensemble is Born's, with the absolute square of the ground state wave function as ensemble probability density function, with the Fisher information functional in the variational principle for Born's ensemble playing the role of the negative of the Gibbs entropy functional in the free-energy variational principle for the classical petit-canonical configurational ensemble.Comment: Corrected version. Accepted for publication in Journal of Mathematical Physic

Interacting classical and quantum particles

We apply Hall and Reginatto's theory of interacting classical and quantum ensembles to harmonically coupled particles, with a view to understanding its experimental implications. This hybrid theory has no free parameters and makes distinctive predictions that should allow it to be experimentally distinguished from quantum mechanics. It also bears on the questions of quantum measurement and quantum gravity.Comment: 7 pages, 6 figure

Flavor Symmetries and The Problem of Squark Degeneracy

If supersymmetry exists at low energies, it is necessary to understand why the squark spectrum exhibits sufficient degeneracy to suppress flavor changing neutral currents. In this note, we point out that gauged horizontal symmetries can yield realistic quark mass matrices, while at the same time giving just barely enough squark degeneracy to account for neutral $K$-meson phenomenology. This approach suggests likely patterns for squark masses, and indicates that there could be significant supersymmetric contributions to $B-\bar{B}$ and $D-\bar{D}$ mixing and CP violation in the $K$ and $B$ systems.Comment: preprint SCIPP 93/04,SLAC-PUB-6147, 14 pages, 4 tables included; uses macro package TABLES.TEX and phyzzx forma

Quantum properties of classical Fisher information

The Fisher information of a quantum observable is shown to be proportional to both (i) the difference of a quantum and a classical variance, thus providing a measure of nonclassicality; and (ii) the rate of entropy increase under Gaussian diffusion, thus providing a measure of robustness. The joint nonclassicality of position and momentum observables is shown to be complementary to their joint robustness in an exact sense.Comment: 16 page

Near-Infrared Classification Spectroscopy: H-band Spectra of Fundamental MK Standards

We present a catalogue of H-band spectra for 85 stars of approximately solar abundance observed at a resolving power of 3000 with the KPNO Mayall 4m FTS. The atlas covers spectral types O7-M5 and luminosity classes I-V as defined on the MK system. We identify both atomic and molecular indices and line-ratios which are temperature and luminosity sensitive allowing spectral classification to be carried out in the H-band. The line ratios permit spectral classification in the presence of continuum excess emission, which is commonly found in pre-main sequence and evolved stars. We demonstrate that with spectra of R = 1000 obtained at SNR > 50 it is possible to derive spectral types within +- 2 subclasses for late-type stars. These data are available electronically through the Astronomical Data Center in addition to being served on the World-Wide-Web.Comment: To appear in the November 20, 1998 issue of ApJ (Volume 508, #1

Power Law Scaling for a System of Interacting Units with Complex Internal Structure

We study the dynamics of a system composed of interacting units each with a complex internal structure comprising many subunits. We consider the case in which each subunit grows in a multiplicative manner. We propose a model for such systems in which the interaction among the units is treated in a mean field approximation and the interaction among subunits is nonlinear. To test the model, we identify a large data base spanning 20 years, and find that the model correctly predicts a variety of empirical results.Comment: 4 pages with 4 postscript figures (uses Revtex 3.1, Latex2e, multicol.sty, epsf.sty and rotate.sty). Submitted to PR