Generalized Euler Angle Parameterization for U(N) with Applications to SU(N) Coset Volume Measures

In a previous paper (math-ph/0205016) an Euler angle parameterization for SU(N) was given. Here we present a generalized Euler angle parameterization for U(N). The formula for the calculation of the volume for U(N), CP(N) as well as other SU(N) and U(N) cosets will also be given. In addition, the mixed and pure state product measures for N-dimensional density matrices under this parameterization will also be derived.Comment: 26 pages, no figures; minor edits, to be published in J. Geom. Phy

Volumes of Compact Manifolds

We present a systematic calculation of the volumes of compact manifolds which appear in physics: spheres, projective spaces, group manifolds and generalized flag manifolds. In each case we state what we believe is the most natural scale or normalization of the manifold, that is, the generalization of the unit radius condition for spheres. For this aim we first describe the manifold with some parameters, set up a metric, which induces a volume element, and perform the integration for the adequate range of the parameters; in most cases our manifolds will be either spheres or (twisted) products of spheres, or quotients of spheres (homogeneous spaces). Our results should be useful in several physical instances, as instanton calculations, propagators in curved spaces, sigma models, geometric scattering in homogeneous manifolds, density matrices for entangled states, etc. Some flag manifolds have also appeared recently as exceptional holonomy manifolds; the volumes of compact Einstein manifolds appear in String theory.Comment: 26 pages, no figures; updated addresses and bibliography. To be published in Rep. Math. Phy

Lifestyles, New Uses, and the Redevelopment of Industrial Heritage Sites: A Case Study of Strijp-S, Eindhoven

As de-industrialisation has left factories vacant and urban living is gaining popularity, redeveloping a former industrial area offers cities a unique residential environment. In order to get insights in the motives of people moving to these areas, this research has studied residents of case study area Strijp-S, their motives of moving there and their lifestyles. Former Philips territory Strijp-S has already been partly redeveloped into a mixed-use creative and culture district and this has been successful as is has been awarded a prestigious prize (NRP Gulden Feniks, 2013) and has become a popular place to live. This study collected data from the residents of Strijp-S. The results of the data collection showed that the main group of Strijp-S residents are young, highly educated singles and couples. Furthermore, a large group moved to this neighborhood from their parental or student homes and thus can be considered as 'starters'. Based upon the activity pattern items from Frenkel, Bendit and Kaplan (2012), four types of lifestyles were discovered: Mellow Morgan, Enthusiastic Elliott, Racing Riley and Sporty Sam. While culture was one of the factors, the lifestyles found in this research mainly distinguished themselves by their attitude towards sport and work. Finally, when examining the motivation of people to move to Strijp-S, it is remarkable how many of the respondents (around 70%) looked for dwellings only in this neighbourhood. In particular, the distance to the city centre and the image of Strijp-S as a creative neighborhood were mentioned to be of importance. Furthermore, residents with a Racing Riley lifestyle and part-time workers tend to choose this neighbourhood for its characteristics and focus less on the dwelling characteristics. So where some studies tend to focus on dwelling characteristics, this research shows that environmental characteristics including the activity types should be taken into account when redeveloping an industrial heritage area. Furthermore, the marketing of the area is important, as the image of Strijp-S as a neighbourhood was often mentioned to be of importance when choosing to move there

Towards a complete, continuous, Wigner function for an ensemble of spins or qubits

We present a new quasi-probability distribution function for ensembles of spin-half particles or qubits that has many properties in common with Wigner's original function for systems of continuous variables. We show that this function provides clear and intuitive graphical representation of a wide variety of states, including Fock states, spin-coherent states, squeezed states, superpositions and statistical mixtures. Unlike previous attempts to represent ensembles of spins/qubits, this distribution is capable of simultaneously representing several angular momentum shells.Comment: 11 pages, 6 figures. If viewed in adobe reader all figures except Fig 2 are interactive. For the non-interactive figures corresponding to those of the published version of this work please see version one of this preprint (which is also a much smaller file

Wigner Functions for Arbitrary Quantum Systems

The possibility of constructing a complete, continuous Wigner function for any quantum system has been a subject of investigation for over 50 years. A key system that has served to illustrate the difficulties of this problem has been an ensemble of spins. Here we present a general and consistent framework for constructing Wigner functions exploiting the underlying symmetries in the physical system at hand. The Wigner function can be used to fully describe any quantum system of arbitrary dimension or ensemble size.Comment: 5 pages, 3 figure

Charged Higgs bosons from the 3-3-1 models and the R(D(∗))\mathcal{R}(D^{(*)}) anomalies

Several anomalies in the semileptonic B-meson decays such as $\mathcal{R}(D^{(*)})$ have been reported by $BABAR$, Belle, and LHCb collaborations recently. In this paper, we investigate the contributions of the charged Higgs bosons from the 3-3-1 models to the $\mathcal{R}(D^{(*)})$ anomalies. We find that, in a wide range of parameter space, the 3-3-1 models might give reasonable explanations to the $\mathcal{R}(D^{(*)})$ anomalies and other analogous anomalies of the B meson's semileptonic decays.Comment: Accpeted by Physical Review