Quantum Phase Transition in a Multi-Level Dot

We discuss electronic transport through a lateral quantum dot close to the singlet-triplet degeneracy in the case of a single conduction channel per lead. By applying the Numerical Renormalization Group, we obtain rigorous results for the linear conductance and the density of states. A new quantum phase transition of the Kosterlitz-Thouless type is found, with an exponentially small energy scale $T^*$ close to the degeneracy point. Below $T^*$, the conductance is strongly suppressed, corresponding to a universal dip in the density of states. This explains recent transport measurements.Comment: 4 pages, 5 eps figures, published versio

Generalized Symmetries of Impulsive Gravitational Waves

We generalize previous \cite{AiBa2} work on the classification of ($C^\infty$) symmetries of plane-fronted waves with an impulsive profile. Due to the specific form of the profile it is possible to extend the group of normal-form-preserving diffeomorphisms to include non-smooth transformations. This extension entails a richer structure of the symmetry algebra generated by the (non-smooth) Killing vectors.Comment: 18 pages, latex2e, no figure

The Poisson-Boltzmann model for implicit solvation of electrolyte solutions: Quantum chemical implementation and assessment via Sechenov coefficients.

We present the theory and implementation of a Poisson-Boltzmann implicit solvation model for electrolyte solutions. This model can be combined with arbitrary electronic structure methods that provide an accurate charge density of the solute. A hierarchy of approximations for this model includes a linear approximation for weak electrostatic potentials, finite size of the mobile electrolyte ions, and a Stern-layer correction. Recasting the Poisson-Boltzmann equations into Euler-Lagrange equations then significantly simplifies the derivation of the free energy of solvation for these approximate models. The parameters of the model are either fit directly to experimental observables-e.g., the finite ion size-or optimized for agreement with experimental results. Experimental data for this optimization are available in the form of Sechenov coefficients that describe the linear dependence of the salting-out effect of solutes with respect to the electrolyte concentration. In the final part, we rationalize the qualitative disagreement of the finite ion size modification to the Poisson-Boltzmann model with experimental observations by taking into account the electrolyte concentration dependence of the Stern layer. A route toward a revised model that captures the experimental observations while including the finite ion size effects is then outlined. This implementation paves the way for the study of electrochemical and electrocatalytic processes of molecules and cluster models with accurate electronic structure methods

The 1958 Pekeris-Accad-WEIZAC Ground-Breaking Collaboration that Computed Ground States of Two-Electron Atoms (and its 2010 Redux)

In order to appreciate how well off we mathematicians and scientists are today, with extremely fast hardware and lots and lots of memory, as well as with powerful software, both for numeric and symbolic computation, it may be a good idea to go back to the early days of electronic computers and compare how things went then. We have chosen, as a case study, a problem that was considered a huge challenge at the time. Namely, we looked at C.L. Pekeris's seminal 1958 work on the ground state energies of two-electron atoms. We went through all the computations ab initio with today's software and hardware, with a special emphasis on the symbolic computations which in 1958 had to be made by hand, and which nowadays can be automated and generalized.Comment: 8 pages, 2 photos, final version as it appeared in the journa

On the consistent solution of the gap--equation for spontaneously broken λΦ4\lambda \Phi^4-theory

We present a self--consistent solution of the finite temperature gap--equation for $\lambda \Phi^4$ theory beyond the Hartree-Fock approximation using a composite operator effective action. We find that in a spontaneously broken theory not only the so--called daisy and superdaisy graphs contribute to the resummed mass, but also resummed non--local diagrams are of the same order, thus altering the effective mass for small values of the latter.Comment: 15 pages of revtex + 3 uuencoded postscript figures, ENSLAPP A-488/9

Assessment in higher education : the potential for a community of practice to improve inter-marker reliability

The design, delivery and assessment of a complete educational scheme, such as a degree programme or a professional qualification course, is a complex matter. Maintaining alignment between the stated aims of the curriculum and the scoring of student achievement is an overarching concern. The potential for drift across individual aspects of an educational scheme (teaching, learning and assessment), together with emerging criticism in extant literature of the reliability of marking processes, suggests that, in practice, maintaining alignment might be more difficult than had previously been assumed. In this paper, the concept of a Community of Practice (CoP) is employed as an analytical lens through which the notion of a markers’ standardisation meeting that focuses on maintaining alignment between the curriculum, the marking scheme and the scoring of student scripts can be critically examined. Given that the aims and subject content of management learning are both multidimensional and contextual, such meetings have the potential to develop a shared approach to the elaboration and application of the marking scheme. A further role of the CoP is in the calibration of markers to accommodate further variations in student responses as they arise in the actual marking process. In this respect, the CoP has both descriptive and prescriptive potential in terms of aiding the development of markers of professional accounting examinations and also, we suggest, within accounting education more generally

Lyapunov exponents, one-dimensional Anderson localisation and products of random matrices

The concept of Lyapunov exponent has long occupied a central place in the theory of Anderson localisation; its interest in this particular context is that it provides a reasonable measure of the localisation length. The Lyapunov exponent also features prominently in the theory of products of random matrices pioneered by Furstenberg. After a brief historical survey, we describe some recent work that exploits the close connections between these topics. We review the known solvable cases of disordered quantum mechanics involving random point scatterers and discuss a new solvable case. Finally, we point out some limitations of the Lyapunov exponent as a means of studying localisation properties.Comment: LaTeX, 23 pages, 3 pdf figures ; review for a special issue on "Lyapunov analysis" ; v2 : typo corrected in eq.(3) & minor change

Wave nucleation rate in excitable systems in the low noise limit

Motivated by recent experiments on intracellular calcium dynamics, we study the general issue of fluctuation-induced nucleation of waves in excitable media. We utilize a stochastic Fitzhugh-Nagumo model for this study, a spatially-extended non-potential pair of equations driven by thermal (i.e. white) noise. The nucleation rate is determined by finding the most probable escape path via minimization of an action related to the deviation of the fields from their deterministic trajectories. Our results pave the way both for studies of more realistic models of calcium dynamics as well as of nucleation phenomena in other non-equilibrium pattern-forming processes

Kaon and Antikaon Production in Heavy Ion Collisions at 1.5 AGeV

At the Kaon Spectrometer KaoS at SIS, GSI the production of kaons and antikaons in heavy ion reactions at a beam energy of 1.5 AGeV has been measured for the collision systems Ni+Ni and Au+Au. The K-/K+ ratio is found to be constant for both systems and as a function of impact parameter but the slopes of K+ and K- spectra differ for all impact parameters. Furthermore the respective polar angle distributions will be presented as a function of centrality.Comment: 4 pages, 4 figures, SQM2001 in Frankfurt, Sept.2001, submitted to Journal of Physics

A practical implementation of the Overlap-Dirac operator

A practical implementation of the Overlap-Dirac operator ${{1+\gamma_5\epsilon(H)}\over 2}$ is presented. The implementation exploits the sparseness of $H$ and does not require full storage. A simple application to parity invariant three dimensional SU(2) gauge theory is carried out to establish that zero modes related to topology are exactly reproduced on the lattice.Comment: Y-axis label in figure correcte