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

Gaussian noise and time-reversal symmetry in non-equilibrium Langevin models

We show that in driven systems the Gaussian nature of the fluctuating force and time-reversibility are equivalent properties. This result together with the potential condition of the external force drastically restricts the form of the probability distribution function, which can be shown to satisfy time-independent relations. We have corroborated this feature by explicitly analyzing a model for the stretching of a polymer and a model for a suspension of non-interacting Brownian particles in steady flow.Comment: 6 pages, submitted to PR

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

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

Spectroscopy on two coupled flux qubits

We have performed spectroscopy measurements on two coupled flux qubits. The qubits are coupled inductively, which results in a $\sigma_1^z\sigma_2^z$ interaction. By applying microwave radiation, we observe resonances due to transitions from the ground state to the first two excited states. From the position of these resonances as a function of the magnetic field applied we observe the coupling of the qubits. The coupling strength agrees well with calculations of the mutual inductance

Multilinear Wavelets: A Statistical Shape Space for Human Faces

We present a statistical model for $3$D human faces in varying expression, which decomposes the surface of the face using a wavelet transform, and learns many localized, decorrelated multilinear models on the resulting coefficients. Using this model we are able to reconstruct faces from noisy and occluded $3$D face scans, and facial motion sequences. Accurate reconstruction of face shape is important for applications such as tele-presence and gaming. The localized and multi-scale nature of our model allows for recovery of fine-scale detail while retaining robustness to severe noise and occlusion, and is computationally efficient and scalable. We validate these properties experimentally on challenging data in the form of static scans and motion sequences. We show that in comparison to a global multilinear model, our model better preserves fine detail and is computationally faster, while in comparison to a localized PCA model, our model better handles variation in expression, is faster, and allows us to fix identity parameters for a given subject.Comment: 10 pages, 7 figures; accepted to ECCV 201

Optimal trap shape for a Bose gas with attractive interactions

Dilute Bose gas with attractive interactions is considered at zero temperature, when practically all atoms are in Bose-Einstein condensate. The problem is addressed aiming at answering the question: What is the optimal trap shape allowing for the condensation of the maximal number of atoms with negative scattering lengths? Simple and accurate analytical formulas are derived allowing for an easy analysis of the optimal trap shapes. These analytical formulas are the main result of the paper.Comment: Latex file, 21 page

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

Quantum many-body dynamics in a Lagrangian frame: II. Geometric formulation of time-dependent density functional theory

We formulate equations of time-dependent density functional theory (TDDFT) in the co-moving Lagrangian reference frame. The main advantage of the Lagrangian description of many-body dynamics is that in the co-moving frame the current density vanishes, while the density of particles becomes independent of time. Therefore a co-moving observer will see the picture which is very similar to that seen in the equilibrium system from the laboratory frame. It is shown that the most natural set of basic variables in TDDFT includes the Lagrangian coordinate, $\bm\xi$, a symmetric deformation tensor $g_{\mu\nu}$, and a skew-symmetric vorticity tensor, $F_{\mu\nu}$. These three quantities, respectively, describe the translation, deformation, and the rotation of an infinitesimal fluid element. Reformulation of TDDFT in terms of new basic variables resolves the problem of nonlocality and thus allows to regularly derive a local nonadiabatic approximation for exchange correlation (xc) potential. Stationarity of the density in the co-moving frame makes the derivation to a large extent similar to the derivation of the standard static local density approximation. We present a few explicit examples of nonlinear nonadiabatic xc functionals in a form convenient for practical applications.Comment: RevTeX4, 18 pages, Corrected final version. The first part of this work is cond-mat/040835