A microscopic model for Josephson currents

A microscopic model of a Josephson junction between two superconducting plates is proposed and analysed. For this model, the nonequilibrium steady state of the total system is explicitly constructed and its properties are analysed. In particular, the Josephson current is rigorously computed as a function of the phase difference of the two plates and the typical properties of the Josephson current are recovered

Some Comments on Multigrid Methods for Computing Propagators

I make three conceptual points regarding multigrid methods for computing propagators in lattice gauge theory: 1) The class of operators handled by the algorithm must be stable under coarsening. 2) Problems related by symmetry should have solution methods related by symmetry. 3) It is crucial to distinguish the vector space $V$ from its dual space $V^*$. All the existing algorithms violate one or more of these principles.Comment: 16 pages, LaTeX plus subeqnarray.sty (included at end), NYU-TH-93/07/0

Goldstone Bosons in Josephson Junctions

For a microscopic model of a Josephson junction the normal coordinates of the two junction Goldstone bosons are constructed and their dynamical spectrum is computed. The explicit dependence on the phase difference of the two superconductors is calculated

Metastability in the BCS model

We discuss metastable states in the mean-field version of the strong coupling BCS-model and study the evolution of a superconducting equilibrium state subjected to a dynamical semi-group with Lindblad generator in detailed balance w.r.t. another equilibrium state. The intermediate states are explicitly constructed and their stability properties are derived. The notion of metastability in this genuine quantum system, is expressed by means of energy-entropy balance inequalities and canonical coordinates of observables

Self-consistent equation for an interacting Bose gas

We consider interacting Bose gas in thermal equilibrium assuming a positive and bounded pair potential $V(r)$ such that 0<\int d\br V(r) = a<\infty. Expressing the partition function by the Feynman-Kac functional integral yields a classical-like polymer representation of the quantum gas. With Mayer graph summation techniques, we demonstrate the existence of a self-consistent relation $\rho (\mu)=F(\mu-a\rho(\mu))$ between the density $\rho$ and the chemical potential $\mu$, valid in the range of convergence of Mayer series. The function $F$ is equal to the sum of all rooted multiply connected graphs. Using Kac's scaling V_{\gamma}(\br)=\gamma^{3}V(\gamma r) we prove that in the mean-field limit $\gamma\to 0$ only tree diagrams contribute and function $F$ reduces to the free gas density. We also investigate how to extend the validity of the self-consistent relation beyond the convergence radius of Mayer series (vicinity of Bose-Einstein condensation) and study dominant corrections to mean field. At lowest order, the form of function $F$ is shown to depend on single polymer partition function for which we derive lower and upper bounds and on the resummation of ring diagrams which can be analytically performed.Comment: 33 pages, 6 figures, submitted to Phys.Rev.

Shopping centre siting and modal choice in Belgium: a destination based analysis

Although modal split is only one of the elements considered in decision-making on new shopping malls, it remarkably often arises in arguments of both proponents and opponents. Today, this is also the case in the debate on the planned development of three major shopping malls in Belgium. Inspired by such debates, the present study focuses on the impact of the location of shopping centres on the travel mode choice of the customers. Our hypothesis is that destination-based variables such as embeddedness in the urban fabric, accessibility and mall size influence the travel mode choice of the visitors. Based on modal split data and location characteristics of seventeen existing shopping centres in Belgium, we develop a model for a more sustainable siting policy. The results show a major influence of the location of the shopping centre in relation to the urban form, and of the size of the mall. Shopping centres that are part of a dense urban fabric, measured through population density, are less car dependent. Smaller sites will attract more cyclists and pedestrians. Interestingly, our results deviate significantly from the figures that have been put forward in public debates on the shopping mall issue in Belgium

Equilibrium states for the Bose gas

The generating functional of the cyclic representation of the CCR (Canonical Commutation Relations) representation for the thermodynamic limit of the grand canonical ensemble of the free Bose gas with attractive boundary conditions is rigorously computed. We use it to study the condensate localization as a function of the homothety point for the thermodynamic limit using a sequence of growing convex containers. The Kac function is explicitly obtained proving non-equivalence of ensembles in the condensate region in spite of the condensate density being zero locally.Comment: 21 pages, no figure

Machining of ceramics and ecological steels using a mill-turn centre equipped with an ultrasonic assisted tooling system

Abstract Today, there is a large demand for the machining of simple and/or complex shaped components made of difficult to cut materials such as ceramics. Recently, there is also a demand to machine new type of steels, having restrictions in chemical composition (e.g. lead and sulphur free) in order to comply with recent governmental EU regulations. This paper first describes on-going and planned research activities on the machining (turning) of these advanced materials. For the machining of various ceramic materials, an ultrasonic assisted tooling system has been designed, manufactured and integrated within the available Mori Seiki NL2000Y/500 mill-turn centre. The developed system has been tested through initial machining experiments on aluminium and ZrO 2 . Second, this paper also briefly describes other on-going and planned research and education activities in which the Mori Seiki NL2000Y/500 is involved. It includes advanced NCprogramming of multi-axis machine tools, energy efficient machining of ecological steels and the development of training programs for 3 rd years mechanical engineering students