Fisher Hartwig determinants, conformal field theory and universality in generalised XX models

We discuss certain quadratic models of spinless fermions on a 1D lattice, and their corresponding spin chains. These were studied by Keating and Mezzadri in the context of their relation to the Haar measures of the classical compact groups. We show how these models correspond to translation invariant models on an infinite or semi-infinite chain, which in the simplest case reduce to the familiar XX model. We give physical context to mathematical results for the entanglement entropy, and calculate the spin-spin correlation functions using the Fisher-Hartwig conjecture. These calculations rigorously demonstrate universality in classes of these models. We show that these are in agreement with field theoretic and renormalization group arguments that we provide

Space station stabilization and control study Final engineering report

Simulation of stabilization and control for spinning, manned space station to provide artificial gravity station environmen

Effects of temperature upon the collapse of a Bose-Einstein condensate in a gas with attractive interactions

We present a study of the effects of temperature upon the excitation frequencies of a Bose-Einstein condensate formed within a dilute gas with a weak attractive effective interaction between the atoms. We use the self-consistent Hartree-Fock Bogoliubov treatment within the Popov approximation and compare our results to previous zero temperature and Hartree-Fock calculations The metastability of the condensate is monitored by means of the $l=0$ excitation frequency. As the number of atoms in the condensate is increased, with $T$ held constant, this frequency goes to zero, signalling a phase transition to a dense collapsed state. The critical number for collapse is found to decrease as a function of temperature, the rate of decrease being greater than that obtained in previous Hartree-Fock calculations.Comment: 4 pages LaTeX, 3 eps figures. To appear as a letter in J. Phys.

Defining and describing what we do: Doctrinal legal research

What exactly is doctrinal legal research? And where does the doctrinal methodology ‘fit’ within the spectrum of scientific and social research methodologies undertaken in other disciplines? The practitioner lawyer of the past had little need to reflect on process. The doctrinal research methodology developed intuitively within the common law - a research method at the core of practice. There was no need to justify or classify it within a broader research framework. Modern academic lawyers are facing a different situation. At a time when competition for limited research funds is becoming more intense, and in which interdisciplinary work is highly valued and non-lawyers are involved in the assessment of grant applications, lawyer-applicants who engage in doctrinal research need to be able to explain their methodology more clearly. Doctrinal scholars need to be more open and articulate about their methods. These methods may be different in different contexts. This paper examines the legal research doctrinal method and its place in recent research dialogue. Some commentators are of the view that the doctrinal method is simply scholarship rather than a separate research methodology. Richard Posner even suggests that law is ‘not a field with a distinct methodology, but an amalgam of applied logic, rhetoric, economics and familiarity with a specialized vocabulary and a particular body of texts, practices, and institutions ..’. Therefore, academic lawyers are beginning to realise that the doctrinal research methodology needs clarification for those outside the legal profession and that a discussion about the standing and place of doctrinal research compared to other methodologies is required

Confounding Issues in the Deadweight Loss of Gift-Giving

When a gift is given, someone other than the final consumer makes the consumption choice. Thus there is a possibility that the gift will not match the preferences of the receiver, i.e., the gift will represent a wise use of the money given the gift-giver's tastes but not necessarily a wise use of money given the recipient's tastes. In other words, gift giving can result in a deadweight loss. This paper addresses and clarifies the discrepancy between Waldfogel's (1993) finding of a deadweight loss from gift giving and Solnick and Hemenway's (1996) finding of a deadweight gain from gift giving. It also builds on some of the concerns raised by Ruffle and Tykocinski (2000).

TB91: The Effect of Acidity, Organic Matter, and Sesquioxide Polymers on the Permanet Charge and pH-Dependent Cation Exchange Capacity of the Caribou Loam Soil.

In this study the components of cation exchange capacity (CEC) were measured in an acid spodosol to determine (1) the increase in KC1-CEC in the whole soil when limed, (2) the contribution of the organic fraction to CEC, and (3) the magnitude of CEC reduction by Al and Fe polymers.https://digitalcommons.library.umaine.edu/aes_techbulletin/1098/thumbnail.jp

The incidence of sudden unexpected death in epilepsy (sudep) in south dublin and wicklow

Patients with epilepsy have a mortality rate higher than that of the general population. Some of this excess mortality is attributable to sudden unexpected death (SUDEP). We examined the incidence of this phenomenon both retrospectively and prospectively in the population of South Dublin and Wicklow over the period May 1992–1995. Cases were ascertained by examination of post-mortem registers of hospitals serving the area studied. Information on cases was sought from hospital records, general practitioners and families. Fifteen cases (10 male, five female) were identified resulting in an overall incidence rate of SUDEP of 1:680/year for the 3 years of the study. This is the only study of incidence of SUDEP conducted in Ireland and our results are in keeping with incidence rates elsewhere in Europe and the USA

Bivariate tt-distribution for transition matrix elements in Breit-Wigner to Gaussian domains of interacting particle systems

Interacting many-particle systems with a mean-field one body part plus a chaos generating random two-body interaction having strength $\lambda$, exhibit Poisson to GOE and Breit-Wigner (BW) to Gaussian transitions in level fluctuations and strength functions with transition points marked by $\lambda=\lambda_c$ and $\lambda=\lambda_F$, respectively; $\lambda_F >> \lambda_c$. For these systems theory for matrix elements of one-body transition operators is available, as valid in the Gaussian domain, with $\lambda > \lambda_F$, in terms of orbitals occupation numbers, level densities and an integral involving a bivariate Gaussian in the initial and final energies. Here we show that, using bivariate $t$-distribution, the theory extends below from the Gaussian regime to the BW regime up to $\lambda=\lambda_c$. This is well tested in numerical calculations for six spinless fermions in twelve single particle states.Comment: 7 pages, 2 figure