Non-universality of chaotic classical dynamics : implications for quantum chaos

It might be anticipated that there is statistical universality in the long-time classical dynamics of chaotic systems, corresponding to the universal agreement between their quantum spectral statistics and random matrix theory. It is argued that no such universality exists. Two statistical properties of long period orbits are considered. The distribution of the phase-space density of periodic orbits of fixed length is shown to have a log-normal distribution. Also, a correlation function of periodic-orbit actions is discussed, which has a semiclassical correspondence to the quantum spectral two-point correlation function. It is shown that bifurcations are a mechanism for creating correlations of periodic-orbit actions. They lead to a result which is non-universal, and which in general may not be an analytic function of the action difference

Semiclassical trace formulae using coherent states

We derive semiclassical trace formulae including Gutzwiller's trace formula using coherent states. This formulation has several advantages over the usual coordinate-space formulation. Using a coherent-state basis makes it immediately obvious that classical periodic orbits make separate contributions to the trace of the quantum-mechanical time evolution operator. In addition, our approach is manifestly canonically invariant at all stages, and leads to the simplest possible derivation of Gutzwiller's formula.Comment: 19 pages, 1 figur

Twelve tips to teaching (legal and ethical aspects of) research ethics/responsible conduct of research

Teaching research ethics is a requirement within modern health science, nursing and medical curricula. We have drawn on our experience of designing, developing and integrating the teaching of research ethics in a new, fully integrated medical school curriculum, delivered using Problem Based Learning and the recent literature relating to the teaching of research ethics to produce the following 12 Top Tips designed to encourage readers to seek opportunities to embed this teaching within a variety of curricula

Psychosocial and material pathways in the relation between income and health: a response to Lynch et al

Summary points: Economic and social circumstances affect health through the physiological effects of their emotional and social meanings and the direct effects of material circumstances. Material conditions do not adequately explain health inequalities in rich countries. The relation between smaller inequalities in income and better population health reflects increased psychosocial wellbeing. In rich countries wellbeing is more closely related to relative income than absolute income. Social dominance, inequality, autonomy, and the quality of social relations have an impact on psychosocial wellbeing and are among the most powerful explanations for the pattern of population health in rich countries

Precise asymptotics for a variable-range hopping model

For a system of localised electron states the DC conductivity vanishes at zero temperature, but localised electrons can conduct at finite temperature. Mott gave a theory for the low-temperature conductivity in terms of a variable-range hopping model, which is hard to analyse. Here we give precise asymptotic results for a modified variable-range hopping model proposed by S. Alexander [Phys. Rev. B 26, 2956 (1982)].Comment: 7 pages, 2 figure

Ergodic and non-ergodic clustering of inertial particles

We compute the fractal dimension of clusters of inertial particles in mixing flows at finite values of Kubo (Ku) and Stokes (St) numbers, by a new series expansion in Ku. At small St, the theory includes clustering by Maxey's non-ergodic 'centrifuge' effect. In the limit of St to infinity and Ku to zero (so that Ku^2 St remains finite) it explains clustering in terms of ergodic 'multiplicative amplification'. In this limit, the theory is consistent with the asymptotic perturbation series in [Duncan et al., Phys. Rev. Lett. 95 (2005) 240602]. The new theory allows to analyse how the two clustering mechanisms compete at finite values of St and Ku. For particles suspended in two-dimensional random Gaussian incompressible flows, the theory yields excellent results for Ku < 0.2 for arbitrary values of St; the ergodic mechanism is found to contribute significantly unless St is very small. For higher values of Ku the new series is likely to require resummation. But numerical simulations show that for Ku ~ St ~ 1 too, ergodic 'multiplicative amplification' makes a substantial contribution to the observed clustering.Comment: 4 pages, 2 figure

Absorption of Energy at a Metallic Surface due to a Normal Electric Field

The effect of an oscillating electric field normal to a metallic surface may be described by an effective potential. This induced potential is calculated using semiclassical variants of the random phase approximation (RPA). Results are obtained for both ballistic and diffusive electron motion, and for two and three dimensional systems. The potential induced within the surface causes absorption of energy. The results are applied to the absorption of radiation by small metal spheres and discs. They improve upon an earlier treatment which used the Thomas-Fermi approximation for the effective potential.Comment: 19 pages (Plain TeX), 2 figures, 1 table (Postscript