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

Commutative POVMs and Fuzzy Observables

In this paper we review some properties of fuzzy observables, mainly as realized by commutative positive operator valued measures. In this context we discuss two representation theorems for commutative positive operator valued measures in terms of projection valued measures and describe, in some detail, the general notion of fuzzification. We also make some related observations on joint measurements.Comment: Contribution to the Pekka Lahti Festschrif

Körperliches Training bei mitochondrialen Erkrankungen

Zusammenfassung: Körperliches Training gilt bei mitochondrialen Myopathien als einer der vielversprechendsten therapeutischen Ansätze. Effektivität und Sicherheit sind bewiesen. Ausdauer- und Krafttraining haben unterschiedliche Wirkungen auf die Muskulatur von Patienten mit mitochondrialer Myopathie: Als therapeutischer Mechanismus des Krafttrainings gilt das so genannte "gene shifting", die trainingsinduzierte Verschiebung des Anteils mutierter mitochondrialer DNS (mtDNS) zugunsten von Wildtyp-mtDNS durch Induktion muskulärer Satellitenzellen. Ausdauertraining regt die mitochondriale Biogenese an und hilft somit, den Circulus vitiosus aus verringertem Mitochondriengehalt, verringerter Kapazität der oxidativen Phosphorylierung, Belastungsintoleranz und daraus resultierender fortschreitender muskulärer Dekonditionierung zu durchbrechen. Die Effektivität und die Sicherheit medikamentöser Induktoren der mitochondrialen Biogenese - möglicherweise in Kombination mit Training - könnten Gegenstand künftiger Untersuchungen sei

Matter-wave vortices in cigar-shaped and toroidal waveguides

We study vortical states in a Bose-Einstein condensate (BEC) filling a cigar-shaped trap. An effective one-dimensional (1D) nonpolynomial Schroedinger equation (NPSE) is derived in this setting, for the models with both repulsive and attractive inter-atomic interactions. Analytical formulas for the density profiles are obtained from the NPSE in the case of self-repulsion within the Thomas-Fermi approximation, and in the case of the self-attraction as exact solutions (bright solitons). A crucially important ingredient of the analysis is the comparison of these predictions with direct numerical solutions for the vortex states in the underlying 3D Gross-Pitaevskii equation (GPE). The comparison demonstrates that the NPSE provides for a very accurate approximation, in all the cases, including the prediction of the stability of the bright solitons and collapse threshold for them. In addition to the straight cigar-shaped trap, we also consider a torus-shaped configuration. In that case, we find a threshold for the transition from the axially uniform state, with the transverse intrinsic vorticity, to a symmetry-breaking pattern, due to the instability in the self-attractive BEC filling the circular trap.Comment: 6 pages, Physical Review A, in pres

Spontaneous symmetry breaking of Bose-Fermi mixtures in double-well potentials

We study the spontaneous symmetry breaking (SSB) of a superfluid Bose-Fermi (BF) mixture in a double-well potential (DWP). The mixture is described by the Gross-Pitaevskii equation (GPE) for the bosons, coupled to an equation for the order parameter of the Fermi superfluid, which is derived from the respective density functional in the unitarity limit (a similar model applies to the BCS regime too). Straightforward SSB in the degenerate Fermi gas loaded into a DWP is impossible, as it requires an attractive self-interaction, while the intrinsic nonlinearity in the Fermi gas is repulsive. Nonetheless, we demonstrate that the symmetry breaking is possible in the mixture with attraction between fermions and bosons, like 40K and 87Rb. Numerical results are represented by dependencies of asymmetry parameters for both components on particle numbers of the mixture, N_F and N_B, and by phase diagrams in the (N_F,N_B) plane, which displays regions of symmetric and asymmetric ground states. The dynamical picture of the SSB, induced by a gradual transformation of the single-well potential into the DWP, is reported too. An analytical approximation is proposed for the case when GPE for the boson wave function may be treated by means of the Thomas-Fermi (TF) approximation. Under a special linear relation between N_F and N_B, the TF approximation allows us to reduce the model to a single equation for the fermionic function, which includes competing repulsive and attractive nonlinear terms. The latter one directly displays the mechanism of the generation of the effective attraction in the Fermi superfluid, mediated by the bosonic component of the mixture.Comment: 10 pages, 6 figures, to be published in Phys. Rev. A (2010)

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

A complete characterization of phase space measurements

We characterize all the phase space measurements for a non-relativistic particle.Comment: 11 pages, latex, no figures, iopart styl

Quantum Homodyne Tomography as an Informationally Complete Positive Operator Valued Measure

We define a positive operator valued measure $E$ on $[0,2\pi]\times R$ describing the measurement of randomly sampled quadratures in quantum homodyne tomography, and we study its probabilistic properties. Moreover, we give a mathematical analysis of the relation between the description of a state in terms of $E$ and the description provided by its Wigner transform.Comment: 9 page

The ISSI international study team on the martian PBL – status report and plan

Dynamical processes in the Martian boundary layer provide the means of communication between surface ice deposits and the free atmosphere, and the means of lifting dust from the surface. The boundary layer is therefore one of the most important components of the Martian climate system. The Martian boundary layer differs from that of the Earth in that it is more strongly forced, it is deeper, and the relative importance of radiative and convective heat fluxes in the lower boundary layer can be quite different. In order to understand the Martian boundary layer, a combination of theoretical, modeling and observational studies are necessary. Interactions between theorists, modelers, and observational scientists are needed to make progress and to provide a basis for analysis of data expected from Phoenix, Mars Science Laboratory, ExoMars and other future landed missions (such as a surface network mission), or missions such as balloons or other aircraft operating in the neutral atmosphere. The prime goal of this project under the auspices of the International Space Science Institute (ISSI) is to review and assess the current knowledge and understanding of Martian planetary boundary layer and its interactions with the surface and free atmosphere. We aim to promote international communication and collaboration to enhance the rate of acquisition of knowledge and understanding. This will be achieved through an International Study Team and publication of overview papers and individual reports on recent advances in this area

Maximally symmetric stabilizer MUBs in even prime-power dimensions

One way to construct a maximal set of mutually unbiased bases (MUBs) in a prime-power dimensional Hilbert space is by means of finite phase-space methods. MUBs obtained in this way are covariant with respect to some subgroup of the group of all affine symplectic phase-space transformations. However, this construction is not canonical: as a consequence, many different choices of covariance sugroups are possible. In particular, when the Hilbert space is $2^n$ dimensional, it is known that covariance with respect to the full group of affine symplectic phase-space transformations can never be achieved. Here we show that in this case there exist two essentially different choices of maximal subgroups admitting covariant MUBs. For both of them, we explicitly construct a family of $2^n$ covariant MUBs. We thus prove that, contrary to the odd dimensional case, maximally covariant MUBs are very far from being unique.Comment: 22 page