Quantum fluctuations and glassy behavior: The case of a quantum particle in a random potential

In this paper we expand our previous investigation of a quantum particle subject to the action of a random potential plus a fixed harmonic potential at a finite temperature T. In the classical limit the system reduces to a well-known ``toy'' model for an interface in a random medium. It also applies to a single quantum particle like an an electron subject to random interactions, where the harmonic potential can be tuned to mimic the effect of a finite box. Using the variational approximation, or alternatively, the limit of large spatial dimensions, together with the use the replica method, and are able to solve the model and obtain its phase diagram in the $T - (\hbar^2/m)$ plane, where $m$ is the particle's mass. The phase diagram is similar to that of a quantum spin-glass in a transverse field, where the variable $\hbar^2/m$ plays the role of the transverse field. The glassy phase is characterized by replica-symmetry-breaking. The quantum transition at zero temperature is also discussed.Comment: revised version, 23 pages, revtex, 5 postscript figures in a separate file figures.u

Quantum Monte Carlo simulations of a particle in a random potential

In this paper we carry out Quantum Monte Carlo simulations of a quantum particle in a one-dimensional random potential (plus a fixed harmonic potential) at a finite temperature. This is the simplest model of an interface in a disordered medium and may also pertain to an electron in a dirty metal. We compare with previous analytical results, and also derive an expression for the sample to sample fluctuations of the mean square displacement from the origin which is a measure of the glassiness of the system. This quantity as well as the mean square displacement of the particle are measured in the simulation. The similarity to the quantum spin glass in a transverse field is noted. The effect of quantum fluctuations on the glassy behavior is discussed.Comment: 23 pages, 7 figures included as eps files, uses RevTeX. Accepted for publication in J. of Physics A: Mathematical and Genera

Replica field theory for a polymer in random media

In this paper we revisit the problem of a (non self-avoiding) polymer chain in a random medium which was previously investigated by Edwards and Muthukumar (EM). As noticed by Cates and Ball (CB) there is a discrepancy between the predictions of the replica calculation of EM and the expectation that in an infinite medium the quenched and annealed results should coincide (for a chain that is free to move) and a long polymer should always collapse. CB argued that only in a finite volume one might see a ``localization transition'' (or crossover) from a stretched to a collapsed chain in three spatial dimensions. Here we carry out the replica calculation in the presence of an additional confining harmonic potential that mimics the effect of a finite volume. Using a variational scheme with five variational parameters we derive analytically for d<4 the result R~(g |ln \mu|)^{-1/(4-d)} ~(g lnV)^{-1/(4-d)}, where R is the radius of gyration, g is the strength of the disorder, \mu is the spring constant associated with the confining potential and V is the associated effective volume of the system. Thus the EM result is recovered with their constant replaced by ln(V) as argued by CB. We see that in the strict infinite volume limit the polymer always collapses, but for finite volume a transition from a stretched to a collapsed form might be observed as a function of the strength of the disorder. For d<2 and for large V>V'~exp[g^(2/(2-d))L^((4-d)/(2-d))] the annealed results are recovered and R~(Lg)^(1/(d-2)), where L is the length of the polymer. Hence the polymer also collapses in the large L limit. The 1-step replica symmetry breaking solution is crucial for obtaining the above results.Comment: Revtex, 32 page

A comparison of the optical properties of radio-loud and radio-quiet quasars

We have made radio observations of 87 optically selected quasars at 5 GHz with the VLA in order to measure the radio power for these objects and hence determine how the fraction of radio-loud quasars varies with redshift and optical luminosity. The sample has been selected from the recently completed Edinburgh Quasar Survey and covers a redshift range of 0.3 < z < 1.5 and an optical absolute magnitude range of -26.5 < M_{B} < -23.5 (h, q_{0} = 1/2). We have also matched up other existing surveys with the FIRST and NVSS radio catalogues and combined these data so that the optical luminosity-redshift plane is now far better sampled than previously. We have fitted a model to the probability of a quasar being radio-loud as a function of absolute magnitude and redshift and from this model infer the radio-loud and radio-quiet optical luminosity functions. The radio-loud optical luminosity function is featureless and flatter than the radio-quiet one. It evolves at a marginally slower rate if quasars evolve by density evolution, but the difference in the rate of evolutions of the two different classes is much less than was previously thought. We show, using Monte-Carlo simulations, that the observed difference in the shape of the optical luminosity functions can be partly accounted for by Doppler boosting of the optical continuum of the radio-loud quasars and explain how this can be tested in the future.Comment: 33 pages, 9 postscript figures, uses the AAS aaspp4 LaTeX style file, to appear in the 1 February 1999 issue of The Astrophysical Journa

NICMOS Observations of Low-Redshift Quasar Host Galaxies

We have obtained Near-Infrared Camera and Multi-Object Spectrometer images of 16 radio quiet quasars observed as part of a project to investigate the ``luminosity/host-mass limit.'' The limit results were presented in McLeod, Rieke, & Storrie-Lombardi (1999). In this paper, we present the images themselves, along with 1- and 2-dimensional analyses of the host galaxy properties. We find that our model-independent 1D technique is reliable for use on ground-based data at low redshifts; that many radio-quiet quasars live in deVaucouleurs-law hosts, although some of the techniques used to determine host type are questionable; that complex structure is found in many of the hosts, but that there are some hosts that are very smooth and symmetric; and that the nuclei radiate at ~2-20% of the Eddington rate based on the assumption that all galaxies have central black holes with a constant mass fraction of 0.6%. Despite targeting hard-to-resolve hosts, we have failed to find any that imply super-Eddington accretion rates.Comment: To appear in ApJ, 28 pages including degraded figures. Download the paper with full-resolutio figures from http://www.astro.wellesley.edu/kmcleod/mm.p

Disorder effects in the quantum Heisenberg model: An Extended Dynamical mean-field theory analysis

We investigate a quantum Heisenberg model with both antiferromagnetic and disordered nearest-neighbor couplings. We use an extended dynamical mean-field approach, which reduces the lattice problem to a self-consistent local impurity problem that we solve by using a quantum Monte Carlo algorithm. We consider both two- and three-dimensional antiferromagnetic spin fluctuations and systematically analyze the effect of disorder. We find that in three dimensions for any small amount of disorder a spin-glass phase is realized. In two dimensions, while clean systems display the properties of a highly correlated spin-liquid (where the local spin susceptibility has a non-integer power-low frequency and/or temperature dependence), in the present case this behavior is more elusive unless disorder is very small. This is because the spin-glass transition temperature leaves only an intermediate temperature regime where the system can display the spin-liquid behavior, which turns out to be more apparent in the static than in the dynamical susceptibility.Comment: 15 pages, 7 figure

Localization of a polymer in random media: Relation to the localization of a quantum particle

In this paper we consider in detail the connection between the problem of a polymer in a random medium and that of a quantum particle in a random potential. We are interested in a system of finite volume where the polymer is known to be {\it localized} inside a low minimum of the potential. We show how the end-to-end distance of a polymer which is free to move can be obtained from the density of states of the quantum particle using extreme value statistics. We give a physical interpretation to the recently discovered one-step replica-symmetry-breaking solution for the polymer (Phys. Rev. E{\bf 61}, 1729 (2000)) in terms of the statistics of localized tail states. Numerical solutions of the variational equations for chains of different length are performed and compared with quenched averages computed directly by using the eigenfunctions and eigenenergies of the Schr\"odinger equation for a particle in a one-dimensional random potential. The quantities investigated are the radius of gyration of a free gaussian chain, its mean square distance from the origin and the end-to-end distance of a tethered chain. The probability distribution for the position of the chain is also investigated. The glassiness of the system is explained and is estimated from the variance of the measured quantities.Comment: RevTex, 44 pages, 13 figure

Search behaviour in electronic document and records management systems: An exploratory investigation and model

Introduction. Organisations implement records management programmes and invest in electronic document and records management systems so that information can be accessed by the right person, at the right time, with the least amount of effort and cost. One of the key factors that predicts the effectiveness of these systems relates to the degree to which users successfully identify the records they wish to retrieve. In this paper we offer a deeper insight into how knowledge workers employ these systems to address their information needs. Method. Four records managers were interviewed to determine how records management principles were applied in their systems. Interviews were also conducted with ten users from each organisation to map their search behaviour. Additionally, protocol analysis was used to observe how participants verbalised their thought processes and actions when they conducted their simple and difficult searches in the systems. Results. A comprehensive model of search behaviour when using electronic document and records management systems was developed from the study. Seven key search stages were identified, illustrating the different ways in which searchers approach their information problem. Conclusions. The study highlights some key differences between users of these systems and other forms of information search behaviour, including different methods of addressing simple or difficult search needs, and user approaches around identifying search strategies. The particular challenges that arise in retrieving information from these systems are also explored

Urban Catholic Elementary Schools: What are the Governance Models?

The closure of nearly half of Catholic elementary schools in the United States since the 1960s has led to the development of many innovative initiatives to stabilize, strengthen, and sustain urban Catholic elementary education. Improving school governance models has been a common agenda of these efforts. This study examined the governance models in use by urban Catholic elementary schools across the United States. Seven major governance models for urban Catholic elementary schools were identified and studied using structured interviews and document analysis. An eighth model, faith-inspired charter schools, is presented as one alternative to a Catholic school. The variety of governance models demonstrates innovation in response to the plight of urban Catholic elementary schools across the country. Common trends across the models are discussed. In short, traditional governance approaches are giving way to more strategic, data-supported models that have the potential t

Analysis of Gamma Rays and Cosmic Muons with a Single Detector

In this paper, we report on the construction and upgrade of a 2002 Lawrence Berkeley National Laboratory (LBNL) Quanknet Cosmic Muons Detector. By adapting this model, we modify the electronics and mechanics to achieve a highly efficient gamma-ray and cosmic-ray detector. Each detector module uses a one-inch-thick scintillator, attached to a photomultiplier tube (PMT) and mounted on a solid aluminum frame. A mechanical support was designed to allow flexible positioning between the two modules. The detector uses scintillation to transform passing radiation into detectable photons that are guided toward a photocathode surface of the PMT, triggering the release of photoelectrons that are then amplified to yield measurable electronic signals. The modules were connected to an electronics section that compared the signals from the two PMTs and logically determined if they were coincidence events. A data-collection device was added for faster count rates and to enable counts for extended times ranging from a few hours to days as needed. Count rates were taken at a variety of distances from the radioactive source, 60Co (cobalt), which produced two gamma rays and a beta particle. To investigate the isotropic behavior of radiation, two detection modules were adjusted to different angles of rotation with respect to each other, and the coincidence counts were measured. The coincidence counts from the modules set at various angles were consistent throughout the angular spectrum, and only lead shielding visibly reduced the number of counts from the radioactive source. The inverse-square-law behavior of radiation has also been considered. The results were such that the number of counts decreased as a function of increasing distance from the source. Furthermore, positioning the detector to point toward the sky in different orientations, we measured cosmic ray muon flux as the angle from the vertical was decreased. In doing so, we scanned different patches of the atmosphere. For the optimum operation during the detection phase, we plateaued both PMTs to single out their best operating gain voltage while eliminating false background noise signals. The detector is more efficient and adaptable in collecting both gamma rays and cosmic-ray muon-flux information