Berry phase, topology, and diabolicity in quantum nano-magnets

A topological theory of the diabolical points (degeneracies) of quantum magnets is presented. Diabolical points are characterized by their diabolicity index, for which topological sum rules are derived. The paradox of the the missing diabolical points for Fe8 molecular magnets is clarified. A new method is also developed to provide a simple interpretation, in terms of destructive interferences due to the Berry phase, of the complete set of diabolical points found in biaxial systems such as Fe8.Comment: 4 pages, 3 figure

Number-of-particle fluctuations in systems with Bose-Einstein condensate

Fluctuations of the number of particles for the dilute interacting gas with Bose-Einstein condensate are considered. It is shown that in the Bogolubov theory these fluctuations are normal. The fluctuations of condensed as well as noncondensed particles are also normal both in canonical and grand canonical ensembles.Comment: Latex file, 12 page

Relative momentum for identical particles

Possible definitions for the relative momentum of identical particles are considered

Investor protection through model case procedures – implementing collective goals and individual rights under the 2012 Amendment of the German Capital Markets Model Case Act (KapMuG)

The German Capital Markets Model Case Act (KapMuG) and its amendment of 2012 highlight some fundamentals of collective redress in civil law countries at the example of model case procedures in the field of investor protection. That is why a survey of the ongoing activities of the European Union in the area of collective redress and of its repercussions on the member state level forms a suitable basis for the following analysis of the 2012 amendment of the KapMuG. It clearly brings into focus a shift from sector-specific regulation with an emphasis on the cross-border aspect of protecting consumers towards a “coherent approach” strengthening the enforcement of EU law. As a result, regulatory policy and collective redress are two sides of the same coin today. With respect to the KapMuG such a development brings about some tension between its aim to aggregate small individual claims as efficiently as possible and the dominant role of individual procedural rights in German civil procedure. This conflict can be illustrated by some specific rules of the KapMuG: its scope of application, the three-tier procedure of a model case procedure, the newly introduced notification of claims and the new opt-out settlement under the amended §§ 17-19

What is the limit ℏ→0\hbar \to 0 of quantum theory ?

An analysis is made of the relation between quantum theory and classical mechanics, in the context of the limit $\hbar \to 0$. Several ways in which this limit may be performed are considered. It is shown that Schr\"odinger's equation for a single particle moving in an external potential $V$ does not, except in special cases, lead, in this limit, to Newton's equation of motion for the particle. This shows that classical mechanics cannot be regarded as emerging from quantum mechanics-at least in this sense-upon straightforward application of the limit $\hbar \to 0$.Comment: 12 pages, no figure

Standardization of serum cholesterol assays by use of serum calibrators and direct addition of Liebermann-Burchard reagent

Serum cholesterol concentrations of subjects in epidemiological studies were measured after direct addition of Liebermann-Burchard reagent; results were calibrated with human serum pools assayed according to Abell et al. (J. Biol. Chem. 195:357-366, 1952). Accuracy and precision were monitored for six years by analysis of internal-control pools and blind external-control pools. For various internal-control pools, the imprecision (CV) of the long-term averages of run means ranged from 0.5 to 0.9%. The within-run CV for internal control and patients' sera was about 1%. For blind control sera with different concentrations (provided by the Centers for Disease Control, Atlanta, GA, over the same period), the average difference per three-month period between the values found and the target values was usually between -0.5% and 0.7% for medium-concentration pools and between -2% and 2% for low- and high-concentration pools (extreme values: -2.4% and 2.5%). The CV per three-month period ranged from 0.6 to 2.7%. Sera from subjects on diets of high or low linoleic acid content were analyzed to study the effect of the fatty acid portion of serum cholesterol esters; the differences between values obtained with the comparison method and the direct method was insignificant on both diets. We conclude that the use of serum calibrators eliminates the bias inherent in the direct method