Positive operator valued measures covariant with respect to an irreducible representation

Given an irreducible representation of a group G, we show that all the covariant positive operator valued measures based on G/Z, where Z is a central subgroup, are described by trace class, trace one positive operators.Comment: 9 pages, Latex2

Quantum symmetries and the Weyl-Wigner product of group representations

In the usual formulation of quantum mechanics, groups of automorphisms of quantum states have ray representations by unitary and antiunitary operators on complex Hilbert space, in accordance with Wigner's Theorem. In the phase-space formulation, they have real, true unitary representations in the space of square-integrable functions on phase-space. Each such phase-space representation is a Weyl-Wigner product of the corresponding Hilbert space representation with its contragredient, and these can be recovered by `factorising' the Weyl-Wigner product. However, not every real, unitary representation on phase-space corresponds to a group of automorphisms, so not every such representation is in the form of a Weyl-Wigner product and can be factorised. The conditions under which this is possible are examined. Examples are presented.Comment: Latex2e file, 37 page

Position and momentum observables on R and on R^3

We characterize all position and momentum observables on R and on R^3. We study some of their operational properties and discuss their covariant joint observables.Comment: 18 page

Unitary representations of super Lie groups and applications to the classification and multiplet structure of super particles

It is well known that the category of super Lie groups (SLG) is equivalent to the category of super Harish-Chandra pairs (SHCP). Using this equivalence, we define the category of unitary representations (UR's) of a super Lie group. We give an extension of the classical inducing construction and Mackey imprimitivity theorem to this setting. We use our results to classify the irreducible unitary representations of semidirect products of super translation groups by classical Lie groups, in particular of the super Poincar\'e groups in arbitrary dimension. Finally we compare our results with those in the physical literature on the structure and classification of super multiplets.Comment: 55 pages LaTeX, some corrections added after comments by Prof. Pierre Delign

X-ray Emission from Magnetically Torqued Disks of Oe/Be Stars

We focus attention on the Oe/Be stars to test the concept that the disks of these stars form by magnetic channeling of wind material toward the equator. Calculations are made of the X-rays expected from the Magnetically Torqued Disk (MTD) model for Be stars discussed by Cassinelli et al. (2002), by Maheswaran (2003), and by Brown et al. (2004). The dominant parameters in the model are the $\beta$ value of the velocity law, the rotation rate of the star, $S_o$, and the ratio of the magnetic field energy density to the disk gravitational energy density, $\gamma$. The model predictions are compared with the $ROSAT$ observations obtained for an O9.5 star $\zeta$ Oph from \Berghofer et al. (1996) and for 7 Be stars from Cohen et al. (1997). Extra considerations are also given here to the well studied Oe star $\zeta$ Oph for which we have $Chandra$ observations of the X-ray line profiles of the triad of He-like lines from the ion Mg XI.Comment: 28 pages with 6 figures. Accepted for publication in Ap

Constructing Extremal Compatible Quantum Observables by Means of Two Mutually Unbiased Bases

We describe a particular class of pairs of quantum observables which are extremal in the convex set of all pairs of compatible quantum observables. The pairs in this class are constructed as uniformly noisy versions of two mutually unbiased bases (MUB) with possibly different noise intensities affecting each basis. We show that not all pairs of MUB can be used in this construction, and we provide a criterion for determining those MUB that actually do yield extremal compatible observables. We apply our criterion to all pairs of Fourier conjugate MUB, and we prove that in this case extremality is achieved if and only if the quantum system Hilbert space is odd-dimensional. Remarkably, this fact is no longer true for general non-Fourier conjugate MUB, as we show in an example. Therefore, the presence or the absence of extremality is a concrete geometric manifestation of MUB inequivalence, that already materializes by comparing sets of no more than two bases at a time

New Challenges For Wind Shock Models: The Chandra Spectrum Of The Hot Star Delta Orionis

The Chandra spectrum of delta Ori A shows emission lines from hydrogen- and helium-like states of Si, Mg, Ne, and O, along with N VII Lyalpha and lines from ions in the range Fe XVII-Fe XXI In contrast to the broad lines seen in zeta Pup and zeta Ori (850 +/- 40 and 1000 +/- 240 km s(-1) half-width at half-maximum [HWHM], respectively), these lines are broadened to only 430 +/- 60 km s(-1) HWHM. This is much lower than the measured wind terminal velocity of 2000 km s(-1). The forbidden, intercombination, and resonance (fir) lines from He-like ions indicate that the majority of the X-ray line emission does not originate at the base of the wind, in agreement with the standard wind shock models for these objects. However, in that model the X-ray emission is distributed throughout an expanding, X-ray-absorbing wind, and it is therefore surprising that the emission lines appear relatively narrow, unshifted, and symmetric. We compare the observed line profiles to recent detailed models for X-ray line pro le generation in hot stars, but none of them offers a fully satisfactory explanation for the observed line profiles

Group Theoretical Quantum Tomography

The paper is devoted to the mathematical foundation of the quantum tomography using the theory of square-integrable representations of unimodular Lie groups.Comment: 13 pages, no figure, Latex2e. Submitted to J.Math.Phy

Streak instability in near-wall turbulence revisited

The regeneration cycle of streaks and streamwise vortices plays a central role in the sustainment of near-wall turbulence. In particular, the streak breakdown phase in the regeneration cycle is the core process in the formation of the streamwise vortices, but its current understanding is limited particularly in a real turbulent environment. This study is aimed at gaining fundamental insight into the underlying physical mechanism of the streak breakdown in the presence of background turbulent fluctuation. We perform a numerical experiment based on direct numerical simulation, in which streaks are artificially generated by a body forcing computed from previous linear theory. Upon increasing the forcing amplitude, the artificially driven streaks are found to generate an intense fluctuation of the wall-normal and spanwise velocities in a fairly large range of amplitudes. This cross-streamwise velocity fluctuation shows its maximum at λ+ x ≈ 200 − 300 (λ+ x is the inner-scaled streamwise wavelength), but it only appears for λ+ x ≲ 3000 − 4000. Further examination with dynamic mode decomposition reveals that the related flow field is composed of sinuous meandering motion of the driven streaks and alternating cross-streamwise velocity structures, clearly reminiscent of sinuous-mode streak instability found in previous studies. Finally, it is shown that these structures are reasonably well aligned along the critical layer of the secondary instability, indicating that the surrounding turbulence does not significantly modify the inviscid inflectional mechanism of the streak breakdown via streak instability and/or streak transient growth