Casimir Energy and Entropy between perfect metal Spheres

We calculate the Casimir energy and entropy for two perfect metal spheres in the large and short separation limit. We obtain nonmonotonic behavior of the Helmholtz free energy with separation and temperature, leading to parameter ranges with negative entropy, and also nonmonotonic behavior of the entropy with temperature and with the separation between the spheres. The appearance of this anomalous behavior of the entropy is discussed as well as its thermodynamic consequences.Comment: 10 pages and 8 figures. Accepted for publication in the Proceedings of the tenth conference on Quantum Field Theory under the influence of external conditions - QFEXT'1

Factors governing macrozoobenthic assemblages in perennial springs in north-western Switzerland

Springs are important freshwater habitats that provide refuge for many rare species. In this study, the fauna and abiotic parameters of 20 perennial springs in north-western Switzerland were investigated. Correlation of abiotic and macrozoobenthos data showed that physicochemical parameters had little impact on macrozoobenthic composition, whereas specific substrate parameters strongly influenced the composition of the macrofauna. Surprisingly, nonmetric multidimensional scaling did not reveal a grouping of springs with similar substrate composition or macrozoobenthic assemblages. However, discharge was identified as the factor significantly determining substrate and the composition of macroinvertebrate assemblages. This justifies the hypothesis that, variation in discharge is the disturbance factor governing the macrofaunal composition temporally and spatially within and between patche

Attractive Casimir Forces in a Closed Geometry

We study the Casimir force acting on a conducting piston with arbitrary cross section. We find the exact solution for a rectangular cross section and the first three terms in the asymptotic expansion for small height to width ratio when the cross section is arbitrary. Though weakened by the presence of the walls, the Casimir force turns out to be always attractive. Claims of repulsive Casimir forces for related configurations, like the cube, are invalidated by cutoff dependence.Comment: An updated version to coincide with the one published December 2005 in PRL. 4 pages, 2 figure

Successful ageing in an area of deprivation: Part 1—A qualitative exploration of the role of life experiences in good health in old age

Objectives: To determine the life histories and current circumstances of healthy and unhealthy older people who share an ecology marked by relative deprivation and generally poor health. Study design: In-depth interview study with a qualitative analysis. Methods: Matched pairs of healthy and unhealthy ‘agers’ were interviewed face-to-face. Healthy ageing was assessed in terms of hospital morbidity and self-reported health. Study participants consisted of 22 pairs (44 individuals), aged 72–89 years, matched for sex, age and deprivation category, and currently resident in the West of Scotland. All study participants were survivors of the Paisley/Renfrew (MIDSPAN) survey, a longitudinal study commenced in 1972 with continuous recording of morbidity and mortality since. Detailed life histories were obtained which focused on family, residence, employment, leisure and health. This information was supplemented by more focused data on ‘critical incidents’, financial situation and position in social hierarchies. Results: Data provided rich insights into life histories and current circumstances but no differences were found between healthy and unhealthy agers. Conclusions: It is important to understand what differentiates individuals who have lived in circumstances characterized by relative deprivation and poor health, yet have aged healthily. This study collected rich and detailed qualitative data. Yet, no important differences were detected between healthy and unhealthy agers. This is an important negative result as it suggests that the phenomenon of healthy ageing and the factors that promote healthy ageing over a lifetime are so complex that they will require even more detailed studies to disentangle

Average ground-state energy of finite Fermi systems

Semiclassical theories like the Thomas-Fermi and Wigner-Kirkwood methods give a good description of the smooth average part of the total energy of a Fermi gas in some external potential when the chemical potential is varied. However, in systems with a fixed number of particles N, these methods overbind the actual average of the quantum energy as N is varied. We describe a theory that accounts for this effect. Numerical illustrations are discussed for fermions trapped in a harmonic oscillator potential and in a hard wall cavity, and for self-consistent calculations of atomic nuclei. In the latter case, the influence of deformations on the average behavior of the energy is also considered.Comment: 10 pages, 8 figure

Level density of a Fermi gas: average growth and fluctuations

We compute the level density of a two--component Fermi gas as a function of the number of particles, angular momentum and excitation energy. The result includes smooth low--energy corrections to the leading Bethe term (connected to a generalization of the partition problem and Hardy--Ramanujan formula) plus oscillatory corrections that describe shell effects. When applied to nuclear level densities, the theory provides a unified formulation valid from low--lying states up to levels entering the continuum. The comparison with experimental data from neutron resonances gives excellent results.Comment: 4 pages, 1 figur

Chaotic Scattering in the Regime of Weakly Overlapping Resonances

We measure the transmission and reflection amplitudes of microwaves in a resonator coupled to two antennas at room temperature in the regime of weakly overlapping resonances and in a frequency range of 3 to 16 GHz. Below 10.1 GHz the resonator simulates a chaotic quantum system. The distribution of the elements of the scattering matrix S is not Gaussian. The Fourier coefficients of S are used for a best fit of the autocorrelation function if S to a theoretical expression based on random--matrix theory. We find very good agreement below but not above 10.1 GHz

Expanded boundary integral method and chaotic time-reversal doublets in quantum billiards

We present the expanded boundary integral method for solving the planar Helmholtz problem, which combines the ideas of the boundary integral method and the scaling method and is applicable to arbitrary shapes. We apply the method to a chaotic billiard with unidirectional transport, where we demonstrate existence of doublets of chaotic eigenstates, which are quasi-degenerate due to time-reversal symmetry, and a very particular level spacing distribution that attains a chaotic Shnirelman peak at short energy ranges and exhibits GUE-like statistics for large energy ranges. We show that, as a consequence of such particular level statistics or algebraic tunneling between disjoint chaotic components connected by time-reversal operation, the system exhibits quantum current reversals.Comment: 18 pages, 8 figures, with 3 additional GIF animations available at http://chaos.fiz.uni-lj.si/~veble/boundary

Semiclassical theory for spatial density oscillations in fermionic systems

We investigate the particle and kinetic-energy densities for a system of $N$ fermions bound in a local (mean-field) potential V(\bfr). We generalize a recently developed semiclassical theory [J. Roccia and M. Brack, Phys. Rev.\ Lett. {\bf 100}, 200408 (2008)], in which the densities are calculated in terms of the closed orbits of the corresponding classical system, to $D>1$ dimensions. We regularize the semiclassical results $(i)$ for the U(1) symmetry breaking occurring for spherical systems at $r=0$ and $(ii)$ near the classical turning points where the Friedel oscillations are predominant and well reproduced by the shortest orbit going from $r$ to the closest turning point and back. For systems with spherical symmetry, we show that there exist two types of oscillations which can be attributed to radial and non-radial orbits, respectively. The semiclassical theory is tested against exact quantum-mechanical calculations for a variety of model potentials. We find a very good overall numerical agreement between semiclassical and exact numerical densities even for moderate particle numbers $N$. Using a "local virial theorem", shown to be valid (except for a small region around the classical turning points) for arbitrary local potentials, we can prove that the Thomas-Fermi functional $\tau_{\text{TF}}[\rho]$ reproduces the oscillations in the quantum-mechanical densities to first order in the oscillating parts.Comment: LaTeX, 22pp, 15 figs, 1 table, to be published in Phys. Rev.

Billiard Systems in Three Dimensions: The Boundary Integral Equation and the Trace Formula

We derive semiclassical contributions of periodic orbits from a boundary integral equation for three-dimensional billiard systems. We use an iterative method that keeps track of the composition of the stability matrix and the Maslov index as an orbit is traversed. Results are given for isolated periodic orbits and rotationally invariant families of periodic orbits in axially symmetric billiard systems. A practical method for determining the stability matrix and the Maslov index is described.Comment: LaTeX, 19 page