Why Two Renormalization Groups are Better than One

The advantages of using more than one renormalization group (RG) in problems with more than one important length scale are discussed. It is shown that: i) using different RG's can lead to complementary information, i.e. what is very difficult to calculate with an RG based on one flow parameter may be much more accessible using another; ii) using more than one RG requires less physical input in order to describe via RG methods the theory as a function of its parameters; iii) using more than one RG allows one to solve problems with more than one diverging length scale. The above points are illustrated concretely in the context of both particle physics and statistical physics using the techniques of environmentally friendly renormalization. Specifically, finite temperature $\lambda\phi^4$ theory, an Ising-type system in a film geometry, an Ising-type system in a transverse magnetic field, the QCD coupling constant at finite temperature and the crossover between bulk and surface critical behaviour in a semi-infinite geometry are considered.Comment: 17 pages LaTex; to be published in the Proceedings of RG '96, Dubn

Properties of Accretion Shocks in Viscous Flows with Cooling Effects

Low angular momentum accretion flows can have standing and oscillating shock waves. We study the region of the parameter space in which multiple sonic points occur in viscous flows in presence of various cooling effects such as bremsstrahlung and Comptonization. We also quantify the parameter space in which shocks are steady or oscillating. We find that cooling induces effects opposite to heating by viscosity even in modifying the topology of the solutions, though one can never be exactly balanced by the other due to their dissimilar dependence on dynamic and thermodynamic parameters. We show that beyond a critical value of cooling, the flow ceases to contain a shock wave.Comment: 18 pages, 12 figures, Accepted for Publication in Int. J. Mod. Phys.

A Family of Controllable Cellular Automata for Pseudorandom Number Generation

In this paper, we present a family of novel Pseudorandom Number Generators (PRNGs) based on Controllable Cellular Automata (CCA) ─ CCA0, CCA1, CCA2 (NCA), CCA3 (BCA), CCA4 (asymmetric NCA), CCA5, CCA6 and CCA7 PRNGs. The ENT and DIEHARD test suites are used to evaluate the randomness of these CCA PRNGs. The results show that their randomness is better than that of conventional CA and PCA PRNGs while they do not lose the structure simplicity of 1-d CA. Moreover, their randomness can be comparable to that of 2-d CA PRNGs. Furthermore, we integrate six different types of CCA PRNGs to form CCA PRNG groups to see if the randomness quality of such groups could exceed that of any individual CCA PRNG. Genetic Algorithm (GA) is used to evolve the configuration of the CCA PRNG groups. Randomness test results on the evolved CCA PRNG groups show that the randomness of the evolved groups is further improved compared with any individual CCA PRNG

N=4 Supersymmetric Yang-Mills on S^3 in Plane Wave Matrix Model at Finite Temperature

We investigate the large N reduced model of gauge theory on a curved spacetime through the plane wave matrix model. We formally derive the action of the N=4 supersymmetric Yang-Mills theory on R \times S^3 from the plane wave matrix model in the large N limit. Furthermore, we evaluate the effective action of the plane wave matrix model up to the two-loop level at finite temperature. We find that the effective action is consistent with the free energy of the N=4 supersymmetric Yang-Mills theory on S^3 at high temperature limit where the planar contributions dominate. We conclude that the plane wave matrix model can be used as a large N reduced model to investigate nonperturbative aspects of the N=4 supersymmetric Yang-Mills theory on R \times S^3.Comment: 31pages: added comments and reference

HST-FOS Observations of M87: Ly-a Emission from the Active Galactic Nucleus

The Faint Object Spectrograph on the Hubble Space Telescope was used to obtain spectra of the central region of M87. These spectra cover the wavelength range 1140 - 1606 Angstrom and have a resolution of about 1 Angstrom. The nuclear continuum is clearly visible in the spectra. The only strong line that is observed is Ly-alpha, which has a velocity width of about 3000 km/sec. There is also a marginal detection of C IV 1549. The ratio of Ly-alpha to C IV in the nuclear spectrum is at least a factor of 2 higher than in a spectrum taken at a position on the disk about 0.6" away from the nucleus by Dopita et al. This enhancement of Ly-alpha at the nucleus could point to significant differences in the properties of the emitting gas and/or the excitation mechanism between the outer and inner disk regions. The strength of the observed Ly-alpha places limits on the properties of the absorbing gas present within M87. For instance, if the hydrogen column at the systemic velocity of M87 is greater than about 10^18 cm^{-2} then it can cover only a small fraction of the line emitting region. Spectra separated by 5 days show a 60% difference in the Ly-alpha flux, but the same continuum level. This could be due to either a displacement between the aperture positions for the two sets of observations, or it could be due to intrinsic variability of the source. The current observations do not strongly favor either of these alternatives. The observations do show, however, that the Ly-alpha line is a useful tracer of kinematics in the M87 nucleus.Comment: 14 pages + 5 figures. LaTeX uses aaspp4.sty. Accepted for publication in the Astrophysical Journa

Quantum error-correcting codes associated with graphs

We present a construction scheme for quantum error correcting codes. The basic ingredients are a graph and a finite abelian group, from which the code can explicitly be obtained. We prove necessary and sufficient conditions for the graph such that the resulting code corrects a certain number of errors. This allows a simple verification of the 1-error correcting property of fivefold codes in any dimension. As new examples we construct a large class of codes saturating the singleton bound, as well as a tenfold code detecting 3 errors.Comment: 8 pages revtex, 5 figure

DIRBE Minus 2MASS: Confirming the CIRB in 40 New Regions at 2.2 and 3.5 Microns

With the release of the 2MASS All-Sky Point Source Catalog, stellar fluxes from 2MASS are used to remove the contribution due to Galactic stars from the intensity measured by DIRBE in 40 new regions in the North and South Galactic polar caps. After subtracting the interplanetary and Galactic foregrounds, a consistent residual intensity of 14.69 +/- 4.49 kJy/sr at 2.2 microns is found. Allowing for a constant calibration factor between the DIRBE 3.5 microns and the 2MASS 2.2 microns fluxes, a similar analysis leaves a residual intensity of 15.62 +/- 3.34 kJy/sr at 3.5 microns. The intercepts of the DIRBE minus 2MASS correlation at 1.25 microns show more scatter and are a smaller fraction of the foreground, leading to a still weak limit on the CIRB of 8.88 +/- 6.26 kJy/sr (1 sigma).Comment: 25 pages LaTeX, 10 figures, 5 tables; Version accepted by the ApJ. Includes minor changes to the text including further discussion of zodiacal light issues and the allowance for variable stars in computing uncertainties in the stellar contribution to the DIRBE intensitie

Lower bound for the quantum capacity of a discrete memoryless quantum channel

We generalize the random coding argument of stabilizer codes and derive a lower bound on the quantum capacity of an arbitrary discrete memoryless quantum channel. For the depolarizing channel, our lower bound coincides with that obtained by Bennett et al. We also slightly improve the quantum Gilbert-Varshamov bound for general stabilizer codes, and establish an analogue of the quantum Gilbert-Varshamov bound for linear stabilizer codes. Our proof is restricted to the binary quantum channels, but its extension of to l-adic channels is straightforward.Comment: 16 pages, REVTeX4. To appear in J. Math. Phys. A critical error in fidelity calculation was corrected by using Hamada's result (quant-ph/0112103). In the third version, we simplified formula and derivation of the lower bound by proving p(Gamma)+q(Gamma)=1. In the second version, we added an analogue of the quantum Gilbert-Varshamov bound for linear stabilizer code

Low-background performance of a monolithic InSb CCD array

A 20 element monolithic InSb charge coupled device (CCD) detector array was measured under low background conditions to assess its potential for orbital astronomical applications. At a temperature of 64 K, previous results for charge transfer efficiency (CTE) were reproduced, and a sensitivity of about 2 x 10 to the minus 15th power joules was measured. At 27 and 6 K, extended integration times were achieved, but CTE was substantially degraded. The noise was approximately 6000 charges, which was in excess of the level where statistical fluctuations from the illumination could be detected. A telescope demonstration was performed showing that the array sensitivity and difficulty of operation were not substantially different from laboratory levels. Ways in which the device could be improved for astronomical applications were discussed

Improvement of stabilizer based entanglement distillation protocols by encoding operators

This paper presents a method for enumerating all encoding operators in the Clifford group for a given stabilizer. Furthermore, we classify encoding operators into the equivalence classes such that EDPs (Entanglement Distillation Protocol) constructed from encoding operators in the same equivalence class have the same performance. By this classification, for a given parameter, the number of candidates for good EDPs is significantly reduced. As a result, we find the best EDP among EDPs constructed from [[4,2]] stabilizer codes. This EDP has a better performance than previously known EDPs over wide range of fidelity.Comment: 22 pages, 2 figures, In version 2, we enumerate all encoding operators in the Clifford group, and fix the wrong classification of encoding operators in version