Quantization on a torus without position operators

We formulate quantum mechanics in the two-dimensional torus without using position operators. We define an algebra with only momentum operators and shift operators and construct irreducible representation of the algebra. We show that it realizes quantum mechanics of a charged particle in a uniform magnetic field. We prove that any irreducible representation of the algebra is unitary equivalent to each other. This work provides a firm foundation for the noncommutative torus theory.Comment: 12 pages, LaTeX2e, the title is changed, minor corrections are made, references are added. To be published in Modern Physics Letters

The effect of stellar-mass black holes on the structural evolution of massive star clusters

We present the results of realistic N-body modelling of massive star clusters in the Magellanic Clouds, aimed at investigating a dynamical origin for the radius-age trend observed in these systems. We find that stellar-mass black holes, formed in the supernova explosions of the most massive cluster stars, can constitute a dynamically important population. If a significant number of black holes are retained (here we assume complete retention), these objects rapidly form a dense core where interactions are common, resulting in the scattering of black holes into the cluster halo, and the ejection of black holes from the cluster. These two processes heat the stellar component, resulting in prolonged core expansion of a magnitude matching the observations. Significant core evolution is also observed in Magellanic Cloud clusters at early times. We find that this does not result from the action of black holes, but can be reproduced by the effects of mass-loss due to rapid stellar evolution in a primordially mass segregated cluster.Comment: Accepted for publication in MNRAS Letters; 2 figures, 1 tabl

Surface Brightness Profiles and Structural Parameters for 53 Rich Stellar Clusters in the Large Magellanic Cloud

We have compiled a pseudo-snapshot data set of two-colour observations from the Hubble Space Telescope archive for a sample of 53 rich LMC clusters with ages 10^6-10^10 yr. We present surface brightness profiles for the entire sample, and derive structural parameters for each cluster, including core radii, and luminosity and mass estimates. Because we expect the results presented here to form the basis for several further projects, we describe in detail the data reduction and surface brightness profile construction processes, and compare our results with those of previous ground-based studies. The surface brightness profiles show a large amount of detail, including irregularities in the profiles of young clusters (such as bumps, dips, and sharp shoulders), and evidence for both double clusters and post core-collapse (PCC) clusters. In particular we find power-law profiles in the inner regions of several candidate PCC clusters, with slopes of approximately -0.7, but showing considerable variation. We estimate that 20 +/- 7 % of the old cluster population of the LMC has entered PCC evolution, a similar fraction to that for the Galactic globular cluster system. In addition, we examine the profile of R136 in detail and show that it is probably not a PCC cluster. We also observe a trend in core radius with age that has been discovered and discussed in several previous publications by different authors. Our diagram has better resolution however, and appears to show a bifurcation at several hundred Myr. We argue that this observed relationship reflects true physical evolution in LMC clusters, with some experiencing small scale core expansion due to mass loss, and others large scale expansion due to some unidentified characteristic or physical process.Comment: Accepted for publication in MNRAS. 24 pages plus 16 figures and 9 pages of profiles. We strongly recommend that the interested reader visit http://www.ast.cam.ac.uk/STELLARPOPS/LMC_clusters/ for on-line data and the full resolution pape

Models of the circumstellar medium of evolving, massive runaway stars moving through the Galactic plane

At least 5 per cent of the massive stars are moving supersonically through the interstellar medium (ISM) and are expected to produce a stellar wind bow shock. We explore how the mass loss and space velocity of massive runaway stars affect the morphology of their bow shocks. We run two-dimensional axisymmetric hydrodynamical simulations following the evolution of the circumstellar medium of these stars in the Galactic plane from the main sequence to the red supergiant phase. We find that thermal conduction is an important process governing the shape, size and structure of the bow shocks around hot stars, and that they have an optical luminosity mainly produced by forbidden lines, e.g. [OIII]. The Ha emission of the bow shocks around hot stars originates from near their contact discontinuity. The H$\alpha$ emission of bow shocks around cool stars originates from their forward shock, and is too faint to be observed for the bow shocks that we simulate. The emission of optically-thin radiation mainly comes from the shocked ISM material. All bow shock models are brighter in the infrared, i.e. the infrared is the most appropriate waveband to search for bow shocks. Our study suggests that the infrared emission comes from near the contact discontinuity for bow shocks of hot stars and from the inner region of shocked wind for bow shocks around cool stars. We predict that, in the Galactic plane, the brightest, i.e. the most easily detectable bow shocks are produced by high-mass stars moving with small space velocities.Comment: 22 pages, 24 figure

What measurable zero point fluctuations can(not) tell us about dark energy

We show that laboratory experiments cannot measure the absolute value of dark energy. All known experiments rely on electromagnetic interactions. They are thus insensitive to particles and fields that interact only weakly with ordinary matter. In addition, Josephson junction experiments only measure differences in vacuum energy similar to Casimir force measurements. Gravity, however, couples to the absolute value. Finally we note that Casimir force measurements have tested zero point fluctuations up to energies of ~10 eV, well above the dark energy scale of ~0.01 eV. Hence, the proposed cut-off in the fluctuation spectrum is ruled out experimentally.Comment: 4 page