Continuity of symplectically adjoint maps and the algebraic structure of Hadamard vacuum representations for quantum fields on curved spacetime

We derive for a pair of operators on a symplectic space which are adjoints of each other with respect to the symplectic form (that is, they are sympletically adjoint) that, if they are bounded for some scalar product on the symplectic space dominating the symplectic form, then they are bounded with respect to a one-parametric family of scalar products canonically associated with the initially given one, among them being its ``purification''. As a typical example we consider a scalar field on a globally hyperbolic spacetime governed by the Klein-Gordon equation; the classical system is described by a symplectic space and the temporal evolution by symplectomorphisms (which are symplectically adjoint to their inverses). A natural scalar product is that inducing the classical energy norm, and an application of the above result yields that its ``purification'' induces on the one-particle space of the quantized system a topology which coincides with that given by the two-point functions of quasifree Hadamard states. These findings will be shown to lead to new results concerning the structure of the local (von Neumann) observable-algebras in representations of quasifree Hadamard states of the Klein-Gordon field in an arbitrary globally hyperbolic spacetime, such as local definiteness, local primarity and Haag-duality (and also split- and type III_1-properties). A brief review of this circle of notions, as well as of properties of Hadamard states, forms part of the article.Comment: 42 pages, LaTeX. The Def. 3.3 was incomplete and this has been corrected. Several misprints have been removed. All results and proofs remain unchange

Resonance absolute quantum reflection at selected energies

The possibility of the resonance reflection (100 % at maximum) is revealed. The corresponding exactly solvable models with the controllable numbers of resonances, their positions and widths are presented.Comment: 5 pages, 2 figure

Efficient preconditioning of the linearized Navier-Stokes equations

We outline a new class of robust and efficient methods for solving subproblems that arise in the linearization and operator splitting of Navier-Stokes equations. We describe a very general strategy for preconditioning that has two basic building blocks; a multigrid V-cycle for the scaler convection-diffusion operator, and a multigrid V-cycle for a pressure Poisson operator. We present numerical experiments illustrating that a simple implementation of our approach leads to an effective and robust solver strategy in that the convergence rate is independent of the grid, robust with respect to the time step, and only deteriorates very slowly as the Reynolds number is increased

Semiclassical initial value calculations of collinear helium atom

Semiclassical calculations using the Herman-Kluk initial value treatment are performed to determine energy eigenvalues of bound and resonance states of the collinear helium atom. Both the $eZe$ configuration (where the classical motion is fully chaotic) and the $Zee$ configuration (where the classical dynamics is nearly integrable) are treated. The classical motion is regularized to remove singularities that occur when the electrons collide with the nucleus. Very good agreement is obtained with quantum energies for bound and resonance states calculated by the complex rotation method.Comment: 24 pages, 3 figures. Submitted to J. Phys.

Quantum field theory and time machines

We analyze the "F-locality condition" (proposed by Kay to be a mathematical implementation of a philosophical bias related to the equivalence principle, we call it the "GH-equivalence principle"), which is often used to build a generalization of quantum field theory to non-globally hyperbolic spacetimes. In particular we argue that the theorem proved by Kay, Radzikowski, and Wald to the effect that time machines with compactly generated Cauchy horizons are incompatible with the F-locality condition actually does not support the "chronology protection conjecture", but rather testifies that the F-locality condition must be modified or abandoned. We also show that this condition imposes a severe restriction on the geometry of the world (it is just this restriction that comes into conflict with the existence of a time machine), which does not follow from the above mentioned philosophical bias. So, one need not sacrifice the GH-equivalence principle to "emend" the F-locality condition. As an example we consider a particular modification, the "MF-locality condition". The theory obtained by replacing the F-locality condition with the MF-locality condition possesses a few attractive features. One of them is that it is consistent with both locality and the existence of time machines.Comment: Revtex, 14 pages, 1 .ps figure. To appear in Phys. Rev. D More detailed discussion is given on the MF-locality condition. Minor corrections in terminolog

Historical-institutionalist perspectives on the development of the EU budget system

The EU budget has only recently started to feature in theories of European integration. Studies typically adopt a historical-institutionalist framework, exploring notions such as path dependency. They have, however, generally been rather aggregated, or coarse-grained, in their approach. The EU budget has thus been treated as a single entity rather than a series of inter-linked institutions. This paper seeks to address these lacunae by adopting a fine-grained approach. This enables us to emphasize the connections that exist between EU budgetary institutions, in both time and space. We show that the initial set of budgetary institutions was unable, over time, to achieve consistently their treaty-based objectives. In response, rather than reform these institutions at potentially high political cost, additional institutions were layered on top of the extant structures. We thus demonstrate how some EU budgetary institutions have remained unchanged, whilst others have been added or changed over time

Orientation and solvatochromism of dyes in liquid crystals.

The orientation and solvatochromism of some dye molecules in a liquid crystal have been investigated. Interactions with the host and the structure of the dye molecule affect the macroscopic alignment of dichroic dye molecules in a liquid crystal: It was observed that some dye molecules show a large bathochromic shift of their absorption maxima in the liquid crystal host relative to the situation in isotropic solvents. It is suggested that this is due to the occurrence of a much weaker reaction field in the anisotropic, rigid host. These dye molecules show little or no apparent order in the anisotropic host despite the observation of a reduction in the electro optic switching time when the dye is present. The highest degree of macroscopic alignment was observed for a merocyanine compound, which showed the smallest solvatochromic shift in the liquid crystal host. These results are discussed in terms of the steric, dipolar and hydrogen bond interactions between the guest and the host

UV Imaging Polarimetry of the peculiar Seyfert 2 galaxy Mrk 477

We present the results of UV imaging polarimetry of the Seyfert 2 galaxy Mrk 477 taken by the Faint Object Camera onboard the Hubble Space Telescope (HST). From a previous HST UV image (lambda ~ 2180A), Mrk 477 has been known to have a pointlike bright UV hotspot in the central region, peculiar among nearby Seyfert 2 galaxies. There are also claims of UV/optical variability, unusual for a Seyfert 2 galaxy. Our data show that there is an off-nuclear scattering region ~ 0."6 (~ 500 pc) NE from the hotspot. The data, after the subtraction of the instrumental effect due to this bright hotspot region, might indicate that the scattered light is also detected in the central 0."2 radius region and is extended to a very wide angle. The hotspot location is consistent with the symmetry center of the PA pattern, which represents the location of the hidden nucleus, but our data do not provide a strong upper limit to the distance between the symmetry center and the hotspot. We have obtained high spatial resolution color map of the continuum which shows that the nuclear spiral arm of 0."4 scale (~ 300pc) is significantly bluer than the off-nuclear mirror and the hotspot region. The nature of the hotspot is briefly discussed.Comment: To appear in Ap