Bound states of PT-symmetric separable potentials

All of the PT-symmetric potentials that have been studied so far have been local. In this paper nonlocal PT-symmetric separable potentials of the form $V(x,y)=i\epsilon[U(x)U(y)-U(-x)U(-y)]$, where $U(x)$ is real, are examined. Two specific models are examined. In each case it is shown that there is a parametric region of the coupling strength $\epsilon$ for which the PT symmetry of the Hamiltonian is unbroken and the bound-state energies are real. The critical values of $\epsilon$ that bound this region are calculated.Comment: 10 pages, 3 figure

Quantum Limits of Measurements Induced by Multiplicative Conservation Laws: Extension of the Wigner-Araki-Yanase Theorem

The Wigner-Araki-Yanase (WAY) theorem shows that additive conservation laws limit the accuracy of measurements. Recently, various quantitative expressions have been found for quantum limits on measurements induced by additive conservation laws, and have been applied to the study of fundamental limits on quantum information processing. Here, we investigate generalizations of the WAY theorem to multiplicative conservation laws. The WAY theorem is extended to show that an observable not commuting with the modulus of, or equivalently the square of, a multiplicatively conserved quantity cannot be precisely measured. We also obtain a lower bound for the mean-square noise of a measurement in the presence of a multiplicatively conserved quantity. To overcome this noise it is necessary to make large the coefficient of variation (the so-called relative fluctuation), instead of the variance as is the case for additive conservation laws, of the conserved quantity in the apparatus.Comment: 8 pages, REVTEX; typo added, to appear in PR

Frequency-dependent reflection of spin waves from a magnetic inhomogeneity induced by a surface DC-current

The reflectivity of a highly localized magnetic inhomogeneity is experimentally studied. The inhomogeneity is created by a dc-current carrying wire placed on the surface of a ferrite film. The reflection of propagating dipole-dominated spin-wave pulses is found to be strongly dependent on the spin-wave frequency if the current locally increases the magnetic field. In the opposite case the frequency dependence is negligible.Comment: 3 pages, 3 figure

Multiwavelength Mass Comparisons of the z~0.3 CNOC Cluster Sample

Results are presented from a detailed analysis of optical and X-ray observations of moderate-redshift galaxy clusters from the Canadian Network for Observational Cosmology (CNOC) subsample of the EMSS. The combination of extensive optical and deep X-ray observations of these clusters make them ideal candidates for multiwavelength mass comparison studies. X-ray surface brightness profiles of 14 clusters with 0.17<z<0.55 are constructed from Chandra observations and fit to single and double beta-models. Spatially resolved temperature analysis is performed, indicating that five of the clusters in this sample exhibit temperature gradients within their inner 60-200 kpc. Integrated spectra extracted within R_2500 provide temperature, abundance, and luminosity information. Under assumptions of hydrostatic equilibrium and spherical symmetry, we derive gas and total masses within R_2500 and R_200. We find an average gas mass fraction within R_200 of 0.136 +/- 0.004, resulting in Omega_m=0.28 +/- 0.01 (formal error). We also derive dynamical masses for these clusters to R_200. We find no systematic bias between X-ray and dynamical methods across the sample, with an average M(dyn)/M(X-ray) = 0.97 +/- 0.05. We also compare X-ray masses to weak lensing mass estimates of a subset of our sample, resulting in a weighted average of M(lens)/M(X-ray) of 0.99 +/- 0.07. We investigate X-ray scaling relationships and find powerlaw slopes which are slightly steeper than the predictions of self-similar models, with an E(z)^(-1) Lx-Tx slope of 2.4 +/- 0.2 and an E(z) M_2500-Tx slope of 1.7 +/- 0.1. Relationships between red-sequence optical richness (B_gc,red) and global cluster X-ray properties (Tx, Lx and M_2500) are also examined and fitted.Comment: Astrophysical Journal, 48 pages, 11 figures, LaTeX. Added correction to surface brightness normalization of MS1512.4+3647, corrections to sample gas mass fractions and calculated value of Omega_m. Figure resolution has been reduced to comply with astro-ph upload requirement

Happiness, environmental protection and market economy

The manufacturing sector is leaving the West for Asia’s low wages and good working culture. Europe would be better off keeping these manufacturing activities, slowing down wage inflation and what is more, letting a young, cheaper workforce from the East settle down within their borders. This would aid in preserving the diverse economic structure which has been characteristic for Europe.Beside the economic growth there are two more concepts which have turned into the “holy cows” of economics during the last fifty years. One is the need to constantly improve labor productivity and the other is increasing competitiveness of nations. The high labor productivity of some countries, induces severe unemployment in the globalized world. In the other hand it is high time we understood that it is not competition, but cooperation that brings more happiness to humanity.Should we still opt for “happiness” and “sanity”, it is quite obvious that we all should, in economists’ terms, define our individual welfare functions corresponding to our own set of values, staying free from the influence of media, advertisements and fashion. The cornerstone to all this is the intelligent citizen who prefers local goods and services

The Variation of Gas Mass Distribution in Galaxy Clusters: Effects of Preheating and Shocks

We investigate the origin of the variation of the gas mass fraction in the core of galaxy clusters, which was indicated by our work on the X-ray fundamental plane. The adopted model supposes that the gas distribution characterized by the slope parameter is related to the preheated temperature. Comparison with observations of relatively hot (~> 3 keV) and low redshift clusters suggests that the preheated temperature is about 0.5-2 keV, which is higher than expected from the conventional galactic wind model and possibly suggests the need for additional heating such as quasars or gravitational heating on the largest scales at high redshift. The dispersion of the preheated temperature may be attributed to the gravitational heating in subclusters. We calculate the central gas fraction of a cluster from the gas distribution, assuming that the global gas mass fraction is constant within a virial radius at the time of the cluster collapse. We find that the central gas density thus calculated is in good agreement with the observed one, which suggests that the variation of gas mass fraction in cluster cores appears to be explained by breaking the self-similarity in clusters due to preheated gas. We also find that this model does not change major conclusions on the fundamental plane and its cosmological implications obtained in previous papers, which strongly suggests that not only for the dark halo but also for the intracluster gas the core structure preserves information about the cluster formation.Comment: 17 pages, to be published in Ap

Design of a fault tolerant airborne digital computer. Volume 1: Architecture

This volume is concerned with the architecture of a fault tolerant digital computer for an advanced commercial aircraft. All of the computations of the aircraft, including those presently carried out by analogue techniques, are to be carried out in this digital computer. Among the important qualities of the computer are the following: (1) The capacity is to be matched to the aircraft environment. (2) The reliability is to be selectively matched to the criticality and deadline requirements of each of the computations. (3) The system is to be readily expandable. contractible, and (4) The design is to appropriate to post 1975 technology. Three candidate architectures are discussed and assessed in terms of the above qualities. Of the three candidates, a newly conceived architecture, Software Implemented Fault Tolerance (SIFT), provides the best match to the above qualities. In addition SIFT is particularly simple and believable. The other candidates, Bus Checker System (BUCS), also newly conceived in this project, and the Hopkins multiprocessor are potentially more efficient than SIFT in the use of redundancy, but otherwise are not as attractive

Preparation of pure and mixed polarization qubits and the direct measurement of figures of merit

Non-classical joint measurements can hugely improve the efficiency with which certain figures of merit of quantum systems are measured. We use such a measurement to determine a particular figure of merit, the purity, for a polarization qubit. In the process we highlight some of subtleties involved in common methods for generating decoherence in quantum optics.Comment: 5 pages, 3 figures, 1 tabl