Convex Functions and Spacetime Geometry

Convexity and convex functions play an important role in theoretical physics. To initiate a study of the possible uses of convex functions in General Relativity, we discuss the consequences of a spacetime $(M,g_{\mu \nu})$ or an initial data set $(\Sigma, h_{ij}, K_{ij})$ admitting a suitably defined convex function. We show how the existence of a convex function on a spacetime places restrictions on the properties of the spacetime geometry.Comment: 26 pages, latex, 7 figures, improved version. some claims removed, references adde

Matrix bandwidth and profile reduction

This program, REDUCE, reduces the bandwidth and profile of sparse symmetric matrices, using row and corresponding column permutations. It is a realization of the algorithm described by the authors elsewhere. It was extensively tested and compared with several other programs and was found to be considerably faster than the others, superior for bandwidth reduction and as satisfactory as any other for profile reduction

Exact Solution of the Infinite-Range Quantum Mattis Model

We have solved the quantum version of the Mattis model with infinite-range interactions. A variational approach gives the exact solution for the infinite-range system, in spite of the non-commutative nature of the quantum spin components; this implies that quantum effects are not predominant in determining the macroscopic properties of the system. Nevertheless, the model has a surprisingly rich phase behaviour, exhibiting phase diagrams with tricritical, three-phase and critical end points.Comment: 14 pages, 11 figure

It's OK not to be OK: Shared Reflections from two PhD Parents in a Time of Pandemic

Adopting an intersectional feminist lens, we explore our identities as single and co‐parents thrust into the new reality of the UK COVID‐19 lockdown. As two PhD students, we present shared reflections on our intersectional and divergent experiences of parenting and our attempts to protect our work and families during a pandemic. We reflect on the social constructions of ‘masculinities’ and ‘emphasized femininities’ as complicated influence on our roles as parents. Finally, we highlight the importance of time and self‐care as ways of managing our shared realities during this uncertain period. Through sharing reflections, we became closer friends in mutual appreciation and solidarity as we learned about each other’s struggles and vulnerabilities

Monte Carlo Eikonal Scattering

Monte Carlo evaluation is used to calculate heavy-ion elastic scattering including the center-of-mass correction and the Coulomb interaction.Angular distributions are presented for a number of nuclear pairs over a wide energy range using nucleon-nucleon scattering parameters taken from phase-shift analyses and densities from independent sources. A technique for the efficient expansion of the Glauber amplitude in partial waves is developed

Many-Body Dynamics and Exciton Formation Studied by Time-Resolved Photoluminescence

The dynamics of exciton and electron-hole plasma populations is studied via time-resolved photoluminescence after nonresonant excitation. By comparing the peak emission at the exciton resonance with the emission of the continuum, it is possible to experimentally identify regimes where the emission originates predominantly from exciton and/or plasma populations. The results are supported by a microscopic theory which allows one to extract the fraction of bright excitons as a function of time.Comment: 11 pages, 5 figure

Charge Symmetry Violation Effects in Pion Scattering off the Deuteron

We discuss the theoretical and experimental situations for charge symmetry violation (CSV) effects in the elastic scattering of pi+ and pi- on deuterium (D) and 3He/3H. Accurate comparison of data for both types of targets provides evidence for the presence of CSV effects. While there are indications of a CSV effect in deuterium, it is much more pronounced in the case of 3He/3H. We provide a description of the CSV effect on the deuteron in terms of single- and double- scattering amplitudes. The Delta-mass splitting is taken into account. Theoretical predictions are compared with existing experimental data for pi-d scattering; a future article will speak to the pi-three nucleon case.Comment: 16 pages of RevTeX, 7 postscript figure

A novel method for evaluating the critical nucleus and the surface tension in systems with first order phase transition

We introduce a novel method for calculating the size of the critical nucleus and the value of the surface tension in systems with first order phase transition. The method is based on classical nucleation theory, and it consists in studying the thermodynamics of a sphere of given radius embedded in a frozen metastable surrounding. The frozen configuration creates a pinning field on the surface of the free sphere. The pinning field forces the sphere to stay in the metastable phase as long as its size is smaller than the critical nucleus. We test our method in two first-order systems, both on a two-dimensional lattice: a system where the parameter tuning the transition is the magnetic field, and a second system where the tuning parameter is the temperature. In both cases the results are satisfying. Unlike previous techniques, our method does not require an infinite volume limit to compute the surface tension, and it therefore gives reliable estimates even by using relatively small systems. However, our method cannot be used at, or close to, the critical point, i.e. at coexistence, where the critical nucleus becomes infinitely large.Comment: 12 pages, 15 figure