Gravitational Instantons from Minimal Surfaces

Physical properties of gravitational instantons which are derivable from minimal surfaces in 3-dimensional Euclidean space are examined using the Newman-Penrose formalism for Euclidean signature. The gravitational instanton that corresponds to the helicoid minimal surface is investigated in detail. This is a metric of Bianchi Type $VII_0$, or E(2) which admits a hidden symmetry due to the existence of a quadratic Killing tensor. It leads to a complete separation of variables in the Hamilton-Jacobi equation for geodesics, as well as in Laplace's equation for a massless scalar field. The scalar Green function can be obtained in closed form which enables us to calculate the vacuum fluctuations of a massless scalar field in the background of this instanton.Comment: One figure available by fax upon request. Abstract missing in original submission. Submitted to Classical and Quantum Gravit

Accretion in Brown Dwarfs: an Infrared View

This paper presents a study of the accretion properties of 19 very low mass objects (Mstar .01-0.1 Msun) in the regions Chamaeleon I and rho-Oph For 8 objects we obtained high resolution Halpha profiles and determined mass accretion rate Macc and accretion luminosity Lacc. Pabeta is detected in emission in 7 of the 10 rho-Oph objects, but only in one in Cha I. Using objects for which we have both a determination of Lacc from Halpha and a Pabeta detection, we show that the correlation between the Pabeta luminosity and luminosity Lacc, found by Muzerolle et al. (1998) for T Tauri stars in Taurus, extends to objects with mass approx 0.03 Msun; L(Pab) can be used to measure Lacc also in the substellar regime. The results were less conclusive for Brgamma, which was detected only in 2 objects, neither of which had an Halpha estimate of Macc. Using the relation between L(Pab) and Lacc we determined the accretion rate for all the objects in our sample (including those with no Halpha spectrum), more than doubling the number of substellar objects with known Macc. When plotted as a function of the mass of the central object together with data from the literature, our results confirm the trend of lower Macc for lower Mstar, although with a large spread. Some of the spread is probably due to an age effect; our very young objects in rho-Oph have on average an accretion rate at least one order of magnitude higher than objects of similar mass in older regions. As a side product, we found that the width of Halpha measured at 10% peak intensity is not only a qualitative indicator of accretion, but can be used to obtain a quantitative estimate of Macc over a large mass range, from T Tauri stars to brown dwarfs. Finally, we found that some of our objects show evidence of mass-loss.Comment: 11 pages, 8 figures, A&A in pres

On Hirschman and log-Sobolev inequalities in mu-deformed Segal-Bargmann analysis

We consider a deformation of Segal-Bargmann space and its transform. We study L^p properties of this transform and obtain entropy-entropy inequalities (Hirschman) and entropy-energy inequalities (log-Sobolev) that generalize the corresponding known results in the undeformed theory.Comment: 42 pages, 3 figure

Berry Phase of a Resonant State

We derive closed analytical expressions for the complex Berry phase of an open quantum system in a state which is a superposition of resonant states and evolves irreversibly due to the spontaneous decay of the metastable states. The codimension of an accidental degeneracy of resonances and the geometry of the energy hypersurfaces close to a crossing of resonances differ significantly from those of bound states. We discuss some of the consequences of these differences for the geometric phase factors, such as: Instead of a diabolical point singularity there is a continuous closed line of singularities formally equivalent to a continuous distribution of `magnetic' charge on a diabolical circle; different classes of topologically inequivalent non-trivial closed paths in parameter space, the topological invariant associated to the sum of the geometric phases, dilations of the wave function due to the imaginary part of the Berry phase and others.Comment: 28 pages Latex, three uuencoded postcript figure

The CRESST Dark Matter Search

The current status of CRESST (Cryogenic Rare Event Search using Superconducting Thermometers) and new results concerning the detector development are presented. The basic technique of CRESST is to search for particle Dark Matter (WIMPS, Weakly Interacting Massive particles) by the measurement of non-thermal phonons as created by WIMP-induced nuclear recoils. Combined with the newly developed method of simultaneous measurement of scintillation light, strong background discrimination is possible, resulting in a substantial increase in WIMP detection sensitivity. The short and long term perspectives of CRESST are discussed.Comment: 12 pages, 6 figure

On the Global Existence of Bohmian Mechanics

We show that the particle motion in Bohmian mechanics, given by the solution of an ordinary differential equation, exists globally: For a large class of potentials the singularities of the velocity field and infinity will not be reached in finite time for typical initial values. A substantial part of the analysis is based on the probabilistic significance of the quantum flux. We elucidate the connection between the conditions necessary for global existence and the self-adjointness of the Schr\"odinger Hamiltonian.Comment: 35 pages, LaTe

Hamiltonian structure of real Monge-Amp\`ere equations

The real homogeneous Monge-Amp\`{e}re equation in one space and one time dimensions admits infinitely many Hamiltonian operators and is completely integrable by Magri's theorem. This remarkable property holds in arbitrary number of dimensions as well, so that among all integrable nonlinear evolution equations the real homogeneous Monge-Amp\`{e}re equation is distinguished as one that retains its character as an integrable system in multi-dimensions. This property can be traced back to the appearance of arbitrary functions in the Lagrangian formulation of the real homogeneous Monge-Amp\`ere equation which is degenerate and requires use of Dirac's theory of constraints for its Hamiltonian formulation. As in the case of most completely integrable systems the constraints are second class and Dirac brackets directly yield the Hamiltonian operators. The simplest Hamiltonian operator results in the Kac-Moody algebra of vector fields and functions on the unit circle.Comment: published in J. Phys. A 29 (1996) 325

European economic constitution and the transformation of democracy : on class and the state of law

In the context of contemporary analyses of the Europe Union as a post-democratic form of economic governance, this article explores the (ordo)liberal character of monetary union as a regime of imposed liberty. The argument holds that rather than forcing the member states into retreat, the economic constitution of Europe strengthens their liberal foundation, securing their utility as the organised force of a mode of social reproduction founded on free labour. It develops the character of the liberal state as the political form of a free market economy with reference to Adam Smith’s classical political economy and the German ordoliberal tradition, which calls for a rule-based system of federated forms of economic governance to secure a free labour economy in conditions of mass democratic aspirations for a freedom from want. It explores the rationale of the ordoliberal distinction between the liberal character and the democratic character of the state and, in this context, assesses the meaning of liberal democracy in a post-democratic Eurozone

Modulation of Human Time Processing by Subthalamic Deep Brain Stimulation

Timing in the range of seconds referred to as interval timing is crucial for cognitive operations and conscious time processing. According to recent models of interval timing basal ganglia (BG) oscillatory loops are involved in time interval recognition. Parkinsońs disease (PD) is a typical disease of the basal ganglia that shows distortions in interval timing. Deep brain stimulation (DBS) of the subthalamic nucleus (STN) is a powerful treatment of PD which modulates motor and cognitive functions depending on stimulation frequency by affecting subcortical-cortical oscillatory loops. Thus, for the understanding of BG-involvement in interval timing it is of interest whether STN-DBS can modulate timing in a frequency dependent manner by interference with oscillatory time recognition processes. We examined production and reproduction of 5 and 15 second intervals and millisecond timing in a double blind, randomised, within-subject repeated-measures design of 12 PD-patients applying no, 10-Hz- and ≥130-Hz-STN-DBS compared to healthy controls. We found under(re-)production of the 15-second interval and a significant enhancement of this under(re-)production by 10-Hz-stimulation compared to no stimulation, ≥130-Hz-STN-DBS and controls. Milliseconds timing was not affected. We provide first evidence for a frequency-specific modulatory effect of STN-DBS on interval timing. Our results corroborate the involvement of BG in general and of the STN in particular in the cognitive representation of time intervals in the range of multiple seconds