Casimir energy density in closed hyperbolic universes

The original Casimir effect results from the difference in the vacuum energies of the electromagnetic field, between that in a region of space with boundary conditions and that in the same region without boundary conditions. In this paper we develop the theory of a similar situation, involving a scalar field in spacetimes with compact spatial sections of negative spatial curvature.Comment: 10 pages. Contribution to the "Fifth Alexander Friedmann International Seminar on Gravitation and Cosmology," Joao Pessoa, Brazil, 2002. Revised version, with altered Abstract and one new referenc

Calorons in SU(3) lattice gauge theory

We examine the semiclassical content of SU(3) Yang Mills theory on the lattice at finite temperature. Employing the cooling method, a set of classical fields is generated from a Monte Carlo ensemble. Various operators are used to inspect this set with respect to topological properties. We find pseudoparticle fields, so-called caloron solutions, possessing the remarkable features of (superpositions of) Kraan-van Baal solutions, i.e. extensions of Harrington-Shepard calorons to generic values of the holonomy.Comment: 14 pages, 16 figure

O2 signature in thin and thick O2-H2O ices

Aims. In this paper we investigate the detectability of the molecular oxygen in icy dust grain mantles towards astronomical objects. Methods. We present a systematic set of experiments with O2-H2O ice mixtures designed to disentangle how the molecular ratio affects the O2 signature in the mid- and near-infrared spectral regions. All the experiments were conducted in a closed-cycle helium cryostat coupled to a Fourier transform infrared spectrometer. The ice mixtures comprise varying thicknesses from 8 $\times$ 10$^{-3}$ to 3 $\mu$m. The absorption spectra of the O2-H2O mixtures are also compared to the one of pure water. In addition, the possibility to detect the O2 in icy bodies and in the interstellar medium is discussed. Results. We are able to see the O2 feature at 1551 cm$^{-1}$ even for the most diluted mixture of H2O : O2 = 9 : 1, comparable to a ratio of O2/H2O = 10 % which has already been detected in situ in the coma of the comet 67P/Churyumov-Gerasimenko. We provide an estimate for the detection of O2 with the future mission of the James Webb Space Telescope (JWST).Comment: 11 pages, 10 figures, article in press, to appear in A&A 201

Unboundedness of adjacency matrices of locally finite graphs

Given a locally finite simple graph so that its degree is not bounded, every self-adjoint realization of the adjacency matrix is unbounded from above. In this note we give an optimal condition to ensure it is also unbounded from below. We also consider the case of weighted graphs. We discuss the question of self-adjoint extensions and prove an optimal criterium.Comment: Typos corrected. Examples added. Cute drawings. Simplification of the main condition. Case of the weight tending to zero more discussed