A Deformation Quantization Theory for Non-Commutative Quantum Mechanics

We show that the deformation quantization of non-commutative quantum mechanics previously considered by Dias and Prata can be expressed as a Weyl calculus on a double phase space. We study the properties of the star-product thus defined, and prove a spectral theorem for the star-genvalue equation using an extension of the methods recently initiated by de Gosson and Luef.Comment: Submitted for publicatio

Quantum theta functions and Gabor frames for modulation spaces

Representations of the celebrated Heisenberg commutation relations in quantum mechanics and their exponentiated versions form the starting point for a number of basic constructions, both in mathematics and mathematical physics (geometric quantization, quantum tori, classical and quantum theta functions) and signal analysis (Gabor analysis). In this paper we try to bridge the two communities, represented by the two co--authors: that of noncommutative geometry and that of signal analysis. After providing a brief comparative dictionary of the two languages, we will show e.g. that the Janssen representation of Gabor frames with generalized Gaussians as Gabor atoms yields in a natural way quantum theta functions, and that the Rieffel scalar product and associativity relations underlie both the functional equations for quantum thetas and the Fundamental Identity of Gabor analysis.Comment: 38 pages, typos corrected, MSC class change

On the Usefulness of Modulation Spaces in Deformation Quantization

We discuss the relevance to deformation quantization of Feichtinger's modulation spaces, especially of the weighted Sjoestrand classes. These function spaces are good classes of symbols of pseudo-differential operators (observables). They have a widespread use in time-frequency analysis and related topics, but are not very well-known in physics. It turns out that they are particularly well adapted to the study of the Moyal star-product and of the star-exponential.Comment: Submitte

Low aerobic mitochondrial energy metabolism in poorly- or undifferentiated neuroblastoma

<p>Abstract</p> <p>Background</p> <p>Succinate dehydrogenase (SDH) has been associated with carcinogenesis in pheochromocytoma and paraganglioma. In the present study we investigated components of the oxidative phosphorylation system in human neuroblastoma tissue samples.</p> <p>Methods</p> <p>Spectrophotometric measurements, immunohistochemical analysis and Western blot analysis were used to characterize the aerobic mitochondrial energy metabolism in neuroblastomas (NB).</p> <p>Results</p> <p>Compared to mitochondrial citrate synthase, SDH activity was severely reduced in NB (n = 14) versus kidney tissue. However no pathogenic mutations could be identified in any of the four subunits of SDH. Furthermore, no genetic alterations could be identified in the two novel SDH assembly factors SDHAF1 and SDH5. Alterations in genes encoding nfs-1, frataxin and isd-11 that could lead to a diminished SDH activity have not been detected in NB.</p> <p>Conclusion</p> <p>Because downregulation of other complexes of the oxidative phosphorylation system was also observed, a more generalized reduction of mitochondrial respiration seems to be present in neuroblastoma in contrast to the single enzyme defect found in hereditary pheochromocytomas.</p

Modelling Social Dynamics (of Obesity) and Thresholds

This paper focuses on the dynamic aspects of individual behavior affected by its social embedding, either at large (society-wide norms or averages) or at a local neighborhood. The emphasis is on how initial conditions can affect the long run outcome and to derive, discuss and apply the conditions for such thresholds. For this purpose, intertemporal social pressure (from peers, from norms, or from fashions) is modelled in two different ways: (i) individual benefit is influenced by the possession of a stock (in the application: weight) and the society wide average, and (ii) individual benefits depend on a norm that follows its own motion, of course driven by agents’ behavior. The topical issue of obesity serves as motivation and corresponding models and examples are presented and analyzed