Density Matrix Renormalization Group Method for the Random Quantum One-Dimensional Systems - Application to the Random Spin-1/2 Antiferromagnetic Heisenberg Chain -

The density matrix renormalization group method is generalized to one dimensional random systems. Using this method, the energy gap distribution of the spin-1/2 random antiferromagnetic Heisenberg chain is calculated. The results are consistent with the predictions of the renormalization group theory demonstrating the effectiveness of the present method in random systems. The possible application of the present method to other random systems is discussed.Comment: 13 pages, 3 figures upon reques

Quantum Fourier transform, Heisenberg groups and quasiprobability distributions

This paper aims to explore the inherent connection among Heisenberg groups, quantum Fourier transform and (quasiprobability) distribution functions. Distribution functions for continuous and finite quantum systems are examined first as a semiclassical approach to quantum probability distribution. This leads to studying certain functionals of a pair of "conjugate" observables, connected via the quantum Fourier transform. The Heisenberg groups emerge naturally from this study and we take a rapid look at their representations. The quantum Fourier transform appears as the intertwining operator of two equivalent representation arising out of an automorphism of the group. Distribution functions correspond to certain distinguished sets in the group algebra. The marginal properties of a particular class of distribution functions (Wigner distributions) arise from a class of automorphisms of the group algebra of the Heisenberg group. We then study the reconstruction of Wigner function from the marginal distributions via inverse Radon transform giving explicit formulas. We consider applications of our approach to quantum information processing and quantum process tomography.Comment: 39 page

On the nature of the z=0 X-ray absorbers: I. Clues from an external group

Absorption lines of OVII at redshift zero are observed in high quality Chandra spectra of extragalactic sightlines. The location of the absorber producing these lines, whether from the corona of the Galaxy or from the Local Group or even larger scale structure, has been a matter of debate. Here we study another poor group like our Local Group to understand the distribution of column density from galaxy to group scales. We show that we cannot yet rule out the group origin of z=0 systems. We further argue that the debate over Galactic vs. extragalactic origin of z=0 systems is premature as they likely contain both components and predict that future higher resolution observations will resolve the z=0 systems into multiple components.Comment: Submitted to ApJ

The Elliptical Galaxy formerly known as the Local Group: Merging the Globular Cluster Systems

Prompted by a new catalogue of M31 globular clusters, we have collected together individual metallicity values for globular clusters in the Local Group. Although we briefly describe the globular cluster systems of the individual Local Group galaxies, the main thrust of our paper is to examine the collective properties. In this way we are simulating the dissipationless merger of the Local Group, into presumably an elliptical galaxy. Such a merger is dominated by the Milky Way and M31, which appear to be fairly typical examples of globular cluster systems of spiral galaxies. The Local Group `Elliptical' has about 700 +/- 125 globular clusters, with a luminosity function resembling the `universal' one. The metallicity distribution has peaks at [Fe/H] ~ -1.55 and -0.64 with a metal-poor to metal-rich ratio of 2.5:1. The specific frequency of the Local Group Elliptical is initially about 1 but rises to about 3, when the young stellar populations fade and the galaxy resembles an old elliptical. The metallicity distribution and stellar population corrected specific frequency are similar to that of some known early type galaxies. Based on our results, we briefly speculate on the origin of globular cluster systems in galaxies.Comment: 22 pages, Latex, 4 figures, 5 tables, submitted to A &

A statistical analysis of the Two Dimensional XMM-Newton Group Survey: The impact of feedback on group properties

(abridged) We present a statistical analysis of 28 nearby galaxy groups from the Two-Dimensional XMM-Newton Group Survey (2dXGS). We focus on entropy and the role of feedback, dividing the sample into cool core (CC) and non cool core (NCC) systems, the first time the latter have been studied in detail in the group regime. The coolest groups have steeper entropy profiles than the warmest systems, and NCC groups have higher central entropy and exhibit more scatter than their CC counterparts. We compare the entropy distribution of the gas in each system to the expected theoretical distribution ignoring non-gravitational processes. In all cases, the observed maximum entropy far exceeds that expected theoretically, and simple models for modifications of the theoretical entropy distribution perform poorly. Applying initial pre-heating, followed by radiative cooling, generally fails to match the low entropy behaviour, and only performs well when the difference between the maximum entropy of the observed and theoretical distributions is small. Successful feedback models need to work differentially to increase the entropy range in the gas, and we suggest two basic possibilities. We analyse the effects of feedback on the entropy distribution, finding systems with a high measure of `feedback impact' to reach higher entropy than their low feedback counterparts and also to show significantly lower central metallicities. If low entropy, metal-rich gas has been boosted to large entropy in the high feedback systems, it must now reside outside 0.5r_500, to remain undetected. We find similar levels of enrichment in both high and low feedback systems, and argue that the lack of extra metals in the highest feedback systems points to an AGN origin for the bulk of the feedback, probably acting within precursor structures.Comment: 24 pages, 21 figures; accepted for publication in MNRA

Kinetic description of avalanching systems

Avalanching systems are treated analytically using the renormalization group (in the self-organized-criticality regime) or mean-field approximation, respectively. The latter describes the state in terms of the mean number of active and passive sites, without addressing the inhomogeneity in their distribution. This paper goes one step further by proposing a kinetic description of avalanching systems making use of the distribution function for clusters of active sites. We illustrate application of the kinetic formalism to a model proposed for the description of the avalanching processes in the reconnecting current sheet of the Earth magnetosphere.Comment: 9 page