Classical solution of the wave equation

The classical limit of wave quantum mechanics is analyzed. It is shown that the general requirements of continuity and finiteness to the solution $\psi(x)=Ae^{i\phi(x)}+ Be^{-i\phi(x)}$, where $\phi(x)=\frac 1\hbar W(x)$ and $W(x)$ is the reduced classical action of the physical system, result in the asymptote of the exact solution and general quantization condition for $W(x)$, which yields the exact eigenvalues of the system.Comment: 8 Pages, 10 Refs, LaTe

Extending Elliptic Curve Chabauty to higher genus curves

We give a generalization of the method of "Elliptic Curve Chabauty" to higher genus curves and their Jacobians. This method can sometimes be used in conjunction with covering techniques and a modified version of the Mordell-Weil sieve to provide a complete solution to the problem of determining the set of rational points of an algebraic curve $Y$.Comment: 24 page

Microlensing of Extended Stellar Sources

We investigate the feasibility of reconstructing the radial intensity profile of extended stellar sources by inverting their microlensed light curves. Using a simple, linear, limb darkening law as an illustration, we show that the intensity profile can be accurately determined, at least over the outer part of the stellar disc, with realistic light curve sampling and photometric errors. The principal requirement is that the impact parameter of the lens be less than or equal to the stellar radius. Thus, the analysis of microlensing events provides a powerful method for testing stellar atmosphere models.Comment: 4 pages LaTeX, to appear in New Astronomy Reviews - proceedings of the Oxford Workshop `Gravitational Lensing: Nature's Own Weighing Scales'. Uses elsart.cls. Paper also available at ftp://info.astro.gla.ac.uk/pub/martin/extended.p

Deconfinement in the presence of a Fermi surface

U(1) gauge theory of non-relativistic fermions interacting via compact U(1) gauge fields in the presence of a Fermi surface appears as an effective field theory in low dimensional quantum antiferromagnetism and heavy fermion liquids. We investigate deconfinement of fermions near the Fermi surface in the effective U(1) gauge theory. Our present analysis benchmarks the recent investigation of quantum electrodynamics in two space and one time dimensions ($QED_3$) by Hermele et al. [Phys. Rev. B {\bf 70}, 214437 (2004)]. Utilizing a renormalization group analysis, we show that the effective U(1) gauge theory with a Fermi surface has a stable charged fixed point. Remarkably, the renormalization group equation for an internal charge $e$ (the coupling strength between non-relativistic fermions and U(1) gauge fields) reveals that the conductivity $\sigma$ of fermions near the Fermi surface plays the same role as the flavor number $N$ of massless Dirac fermions in $QED_3$. This leads us to the conclusion that if the conductivity of fermions is sufficiently large, instanton excitations of U(1) gauge fields can be suppressed owing to critical fluctuations of the non-relativistic fermions at the charged fixed point. As a result a critical field theory of non-relativistic fermions interacting via noncompact U(1) gauge fields is obtained at the charged fixed point

Quantum replica approach to the under-screened Kondo model

We extend the Schwinger boson large N treatment of the underscreened Kondo model in a way that correctly captures the finite elastic phase shift in the singular Fermi liquid. The new feature of the approach, is the introduction of a flavor quantum number with K possible values, associated with the Schwinger boson representation. The large N limit is taken maintaining the ratio k=K/N fixed. This approach differs from previous approaches, in that we do not explicitly enforce a constraint on the spin representation of the Schwinger bosons. Instead, the energetics of the Kondo model cause the bosonic degrees of freedom to ``self assemble'' into a ground-state in which the spins of K bosons and N-K conduction electrons are antisymmetrically arranged into a Kondo singlet. With this device, the large N limit can be taken, in such a way that a fraction K/N of the Abrikosov Suhl resonance is immersed inside the Fermi sea. We show how this method can be used to model the full energy dependence of the singular Abrikosov Suhl resonance in the underscreened Kondo model and the field-dependent magnetization.Comment: Revised draft, with plots explicitly showing logarithmic scaling of inverse coupling constant. Small corrections prior to submission to journa

T-violation tests for relativity principles

We consider the implications of a violation of the equivalence principle or of Lorentz invariance in the neutrino sector for the T-asymmetry $\Delta P_T \equiv P(\nu_{\alpha} \to \nu_{\beta}) - P(\nu_{\beta} \to \nu_{\alpha})$ in a three-flavour framework. We find that additional mixing due to these mechanisms, while obeying all present bounds, can lead to a substantial enhancement, suppression, and/or sign change in $\Delta P_T$ for the preferred energies and baselines of a neutrino factory. This in turn allows for the possibility of improving existing constraints by several orders of magnitude.Comment: 2 pages; Talk given at the 4th NuFact '02 Workshop (Neutrino Factories Based On Muon Storage Rings), 1-6 Jul 2002, London, England; To appear in proceeding

Co-operative Kondo Effect in the two-channel Kondo Lattice

We discuss the possibility of a co-operative Kondo effect driven by channel interference in a Kondo lattice where local moments are coupled to a single Fermi sea via two orthogonal scattering channels. In this situation, the channel quantum number is not conserved. We argue that the absence of channel conservation causes the Kondo effect in the two channels to constructively interfere, giving rise to a superconducting condensate of composite pairs, formed between the local moments and the conduction electrons. Our arguments are based on the observation that a heavy Fermi surface gives rise to zero modes for Kondo singlets to fluctuate between screening channels of different symmetry, producing a divergent composite pair susceptibility. Secondary screening channels couple to these divergent fluctuations, promoting an instability into a state with long-range composite order. We present detailed a detailed mean-field theory for this superconducting phase, and discuss the possible implications for heavy fermion physics.Comment: 23 double column pages. 9 fig

Gender and educational leadership in England: a comparison of secondary headteachers' views over time

In the context of gender being a barrier to accessing leadership, this paper presents a comparison of the views of men and women head teacher (principals) of secondary schools in England in the 1990s and in 2004. The same survey instrument was used on both occasions. The perceptions of the head teachers show change in some areas and no change in others. Overall, women are more likely to become head teachers and are now less likely to be categorised into pastoral roles, but in some cases women still meet prejudice from governors and others in the wider community. Women head teachers are more likely to have partners and children than in the 1990s, sharing equally or carrying most of the domestic responsibilities, whereas male colleagues are most likely to have partners who take the majority of responsibility in the home. Essentialist stereotypes about women and men as leaders still prevail, although both the women and men head teachers see themselves as adopting a traditionally ‘feminine’ style of leadership. Women head teachers are likely to see some benefits in being a woman in a role stereotypically associated with men. However, there has been an increase in the proportion of women who feel that they have to prove their worth as a leader, and this may be linked with increased levels of accountability in schools