Critical bubbles and implications for critical black strings

We demonstrate the existence of gravitational critical phenomena in higher dimensional electrovac bubble spacetimes. To this end, we study linear fluctuations about families of static, homogeneous spherically symmetric bubble spacetimes in Kaluza-Klein theories coupled to a Maxwell field. We prove that these solutions are linearly unstable and posses a unique unstable mode with a growth rate that is universal in the sense that it is independent of the family considered. Furthermore, by a double analytical continuation this mode can be seen to correspond to marginally stable stationary modes of perturbed black strings whose periods are integer multiples of the Gregory-Laflamme critical length. This allow us to rederive recent results about the behavior of the critical mass for large dimensions and to generalize them to the charged black string case.Comment: A reference to unpublished work for the case q=2, by J. Hovdebo adde

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

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

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

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

Isolated singularities for some types of curvature equations

AbstractWe consider the removability of isolated singularities for the curvature equations of the form Hk[u]=0, which is determined by the kth elementary symmetric function, in an n-dimensional domain. We prove that, for 1⩽k⩽n−1, isolated singularities of any viscosity solutions to the curvature equations are always removable, provided the solution can be extended continuously at the singularities. We also consider the class of “generalized solutions” and prove the removability of isolated singularities

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

Final report on the search for neutrinoless double-β decay of 76Ge from the Gotthard underground experiment

We report here on the final results of a search for Ge-76 double-beta decay conducted in the Gotthard underground laboratory. The detector consists of an array of eight high-purity natural germanium crystals totaling 1095 cm^3 fiducial volume. The accumulated data set represents a sensitivity of 10.0 kg yr. No indication of neutrinoless double-beta decay was found. The measured half-life limits are T1/2(0+ --> 0+) > 6.0(3.3) x 10^(23) yr for the transition to the ground state and T1/2(0+ --> 2+) > 1.4(0.65) x 10^(23) yr for the transition to the first excited state at 68% (90%) C.L. From these results we derive an upper limit for the Majorana mass of the neutrino in the range of 1.8 to 6.7 eV depending on matrix-element calculations. The same results allow limits to be set for the right-handed-current parameters: < 2.2 x 10^(-8)

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

New limit on neutrinoless double β decay in ^(136)Xe with a time projection chamber

A xenon time projection chamber with an active volume of 207 L has been built to study neutrinoless double β decay in ^(136)Xe. Data were taken in the Gotthard Underground Laboratory, with 5 atm of xenon enriched to 62.5% in ^(136)Xe. From 3380 h of data, no evidence has been found for the 0ν 0^(+)→0^(+) transition. Half-life limits of T_(1/2)^(0ν)>2.5(4.9)×10^(23) yr in the mass-mechanism mode and T_(1/2)^(0ν)>1.7(3.2)×10^(23) yr in the right-handed-current mode, at the 90(68)% C.L., were derived. An upper limit for the Majorana neutrino mass parameter was deduced