Exact Solution of a One-Dimensional Multicomponent Lattice Gas with Hyperbolic Interaction

We present the exact solution to a one-dimensional multicomponent quantum lattice model interacting by an exchange operator which falls off as the inverse-sinh-square of the distance. This interaction contains a variable range as a parameter, and can thus interpolate between the known solutions for the nearest-neighbor chain, and the inverse-square chain. The energy, susceptibility, charge stiffness and the dispersion relations for low-lying excitations are explicitly calculated for the absolute ground state, as a function of both the range of the interaction and the number of species of fermions.Comment: 13 REVTeX pages + 5 uuencoded figures, UoU-003059

Fresh Pastures

Stor

The qualifications/jobs mismatch in Scotland

Two important features within the Scottish economy over recent decades have been the investments made in education and training and the subsequent and consequential enhancement of the skills profile of the workforce (Scottish Government, 2007a)

Algorithms to solve the Sutherland model

We give a self-contained presentation and comparison of two different algorithms to explicitly solve quantum many body models of indistinguishable particles moving on a circle and interacting with two-body potentials of $1/\sin^2$-type. The first algorithm is due to Sutherland and well-known; the second one is a limiting case of a novel algorithm to solve the elliptic generalization of the Sutherland model. These two algorithms are different in several details. We show that they are equivalent, i.e., they yield the same solution and are equally simple.Comment: 15 pages, LaTe

Solitons in the Calogero-Sutherland Collective-Field Model

In the Bogomol'nyi limit of the Calogero-Sutherland collective-field model we find static-soliton solutions. The solutions of the equations of motion are moving solitons, having no static limit for \l>1. They describe holes and lumps, depending on the value of the statistical parametar \l.Comment: minor correction

The National Minimum Wage and In-work Poverty

The analysis presented in this paper considers the impact on poverty rates of the Labour government�s tax and benefit policy changes in combination with the introduction of the National Minimum Wage (NMW). It examines the contribution of the NMW to direct poverty reduction and to �making work pay�. It concludes that the main contribution made by the NMW to poverty reduction at the household level is probably through its role in underpinning the operation of in-work top-up benefits

A Generic Approach to Searching for Jacobians

We consider the problem of finding cryptographically suitable Jacobians. By applying a probabilistic generic algorithm to compute the zeta functions of low genus curves drawn from an arbitrary family, we can search for Jacobians containing a large subgroup of prime order. For a suitable distribution of curves, the complexity is subexponential in genus 2, and O(N^{1/12}) in genus 3. We give examples of genus 2 and genus 3 hyperelliptic curves over prime fields with group orders over 180 bits in size, improving previous results. Our approach is particularly effective over low-degree extension fields, where in genus 2 we find Jacobians over F_{p^2) and trace zero varieties over F_{p^3} with near-prime orders up to 372 bits in size. For p = 2^{61}-1, the average time to find a group with 244-bit near-prime order is under an hour on a PC.Comment: 22 pages, to appear in Mathematics of Computatio