Foldy-Wouthuysen Transformation for a Spinning Particle with Anomalous Magnetic Moment

We study the Foldy-Wouthuysen transformation for a pseudoclassical particle with anomalous magnetic moment in an external, stationary electromagnetic field. We show that the transformation can be expressed in a closed form for neutral particles in purely electrostatic fields and for neutral and charged particles in external magnetostatic fields. The explicit expressions of the diagonalized Hamiltonians are calculated.Comment: 10 page

Spinning particle in an external linearized gravitational wave field

We study the interaction of a scalar and a spinning particle with a coherent linearized gravitational wave field treated as a classical spin two external field. The spin degrees of freedom of the spinning particle are described by skew-commuting variables. We derive the explicit expressions for the eigenfunctions and the Green's functions of the theory. The discussion is exact within the approximation of neglecting radiative corrections and we prove that the result is completely determined by the semiclassical contribution.Comment: 11 page

Local Variational Principle

A generalization of the Gibbs-Bogoliubov-Feynman inequality for spinless particles is proven and then illustrated for the simple model of a symmetric double-well quartic potential. The method gives a pointwise lower bound for the finite-temperature density matrix and it can be systematically improved by the Trotter composition rule. It is also shown to produce groundstate energies better than the ones given by the Rayleigh-Ritz principle as applied to the groundstate eigenfunctions of the reference potentials. Based on this observation, it is argued that the Local Variational Principle performs better than the equivalent methods based on the centroid path idea and on the Gibbs-Bogoliubov-Feynman variational principle, especially in the range of low temperatures.Comment: 15 pages, 5 figures, one more section adde

Optimization of extraction of drugs containing polyphenols using an innovative technique

The role of polyphenols in human health nowadays is well established and these natural products, found in many plant species, are the active ingredients of drugs, food supplements and cosmetics. Extraction procedure is pivotal to obtain high quality herbal products but paradoxically this factor is often underrated and obsolete techniques are used. In this work we compared the classic and most used method of maceration and an innovative and standardized technique of extraction, Estrattore Naviglio((R)), processing ten common medicinal plants containing polyphenols and for each analysing specific biological markers such as flavonoids, anthocyanosides and caffeic derivatives in addition to total polyphenols content. Estrattore Naviglio((R)) guaranteed a significant improvement of the chemical quality of extracts combining effectiveness with rapidity and reproducibility. In this work we further investigated the optimization of drug extractions by replicating operations varying parameters setting on Estrattore Naviglio((R)) instrument

Quantum Double and Differential Calculi

We show that bicovariant bimodules as defined by Woronowicz are in one to one correspondence with the Drinfeld quantum double representations. We then prove that a differential calculus associated to a bicovariant bimodule of dimension n is connected to the existence of a particular (n+1)--dimensional representation of the double. An example of bicovariant differential calculus on the non quasitriangular quantum group E_q(2) is developed. The construction is studied in terms of Hochschild cohomology and a correspondence between differential calculi and 1-cocycles is proved. Some differences of calculi on quantum and finite groups with respect to Lie groups are stressed.Comment: Revised version with added cohomological analysis. 14 pages, plain te

Two fermion relativistic bound states: hyperfine shifts

We discuss the hyperfine shifts of the Positronium levels in a relativistic framework, starting from a two fermion wave equation where, in addition to the Coulomb potential, the magnetic interaction between spins is described by a Breit term. We write the system of four first order differential equations describing this model. We discuss its mathematical features, mainly in relation to possible singularities that may appear at finite values of the radial coordinate. We solve the boundary value problems both in the singular and non singular cases and we develop a perturbation scheme, well suited for numerical computations, that allows to calculate the hyperfine shifts for any level, according to well established physical arguments that the Breit term must be treated at the first perturbative order. We discuss our results, comparing them with the corresponding values obtained from semi-classical expansions.Comment: 16 page

Kinetic energy of solid neon by Monte Carlo with improved Trotter- and finite-size extrapolation

The kinetic energy of solid neon is calculated by a path-integral Monte Carlo approach with a refined Trotter- and finite-size extrapolation. These accurate data present significant quantum effects up to temperature T=20 K. They confirm previous simulations and are consistent with recent experiments.Comment: Text and figures revised for minor corrections (4 pages, 3 figures included by psfig

Multicanonical Multigrid Monte Carlo

To further improve the performance of Monte Carlo simulations of first-order phase transitions we propose to combine the multicanonical approach with multigrid techniques. We report tests of this proposition for the $d$-dimensional $\Phi^4$ field theory in two different situations. First, we study quantum tunneling for $d = 1$ in the continuum limit, and second, we investigate first-order phase transitions for $d = 2$ in the infinite volume limit. Compared with standard multicanonical simulations we obtain improvement factors of several resp. of about one order of magnitude.Comment: 12 pages LaTex, 1 PS figure appended. FU-Berlin preprint FUB-HEP 9/9

Retrieval and classification methods for textured 3D models: a comparative study

International audienceThis paper presents a comparative study of six methods for the retrieval and classification of tex-tured 3D models, which have been selected as representative of the state of the art. To better analyse and control how methods deal with specific classes of geometric and texture deformations, we built a collection of 572 synthetic textured mesh models, in which each class includes multiple texture and geometric modifications of a small set of null models. Results show a challenging, yet lively, scenario and also reveal interesting insights in how to deal with texture information according to different approaches, possibly working in the CIELab as well as in modifications of the RGB colour space