Self-Adjoint Extensions of Dirac Operator with Coulomb Potential

In this note we give a concise review of the present state-of-art for the problem of self-adjoint realisations for the Dirac operator with a Coulomb-like singular scalar potential $V(\vec x)=\phi(\vec x) I_4$. We try to follow the historical and conceptual path that leads to the present understanding of the problem and to highlight the techniques employed and the main ideas. In the final part we outline a few major open questions that concern the topical problem of the multiplicity of self-adjoint realisations of the model, and which are worth addressing in the future.Comment: 17 page

On Geometric Quantum Confinement in Grushin-type Manifolds

We study the problem of so-called geometric quantum confinement in a class of two-dimensional incomplete Riemannian manifold with metric of Grushin type. We employ a constant-fibre direct integral scheme, in combination with Weyl's analysis in each fibre, thus fully characterising the regimes of presence and absence of essential self-adjointness of the associated Laplace-Beltrami operator.Comment: 16 pages, 2 figure

Superselection Structure of Massive Quantum Field Theories in 1+1 Dimensions

We show that a large class of massive quantum field theories in 1+1 dimensions, characterized by Haag duality and the split property for wedges, does not admit locally generated superselection sectors in the sense of Doplicher, Haag and Roberts. Thereby the extension of DHR theory to 1+1 dimensions due to Fredenhagen, Rehren and Schroer is vacuous for such theories. Even charged representations which are localizable only in wedge regions are ruled out. Furthermore, Haag duality holds in all locally normal representations. These results are applied to the theory of soliton sectors. Furthermore, the extension of localized representations of a non-Haag dual net to the dual net is reconsidered. It must be emphasized that these statements do not apply to massless theories since they do not satisfy the above split property. In particular, it is known that positive energy representations of conformally invariant theories are DHR representations.Comment: latex2e, 21 pages. Final version, to appear in Rev. Math. Phys. Some improvements of the presentation, but no essential change

Discrete spectra for critical Dirac-Coulomb Hamiltonians

The one-particle Dirac Hamiltonian with Coulomb interaction is known to be realised, in a regime of large (critical) couplings, by an infinite multiplicity of distinct self-adjoint operators, including a distinguished, physically most natural one. For the latter, Sommerfeld's celebrated fine structure formula provides the well-known expression for the eigenvalues in the gap of the continuum spectrum. Exploiting our recent general classification of all other self-adjoint realisations, we generalise Sommerfeld's formula so as to determine the discrete spectrum of all other self-adjoint versions of the Dirac-Coulomb Hamiltonian. Such discrete spectra display naturally a fibred structure, whose bundle covers the whole gap of the continuum spectrum.Comment: 24 pages, 3 figures. Version published on Journal of Mathematical Physics (2018

An Alternative to Matter Localization in the "Brane World": An Early Proposal and its Later Improvements

Here we place the Latex typeset of the paper M. Pavsic, Phys. Lett. A116 (1986) 1-5. In the paper we presented the picture that our spacetime is a 3-brane moving in a higher dimensional space. The dynamical equations were derived from the action which is just that for the usual Dirac-Nambu-Goto $p$-brane. We also considered the case where not only one, but many branes of various dimensionalities are present, and showed that their intersections with the 3-brane manifest as matter in 4-dimensional spacetime. We considered a particular case, where the intersections behaved as point particles, and found out that they follow the geodesics on the 3-brane worldsheet (identified with our spacetime). In a series of subsequent papers the original idea has been further improved and developped. This is discussed in a note at the end, where it is also pointed out that such a model resolves the problem of massive matter confinement on the brane, recently discussed by Rubakov et al. and Mueck et al.Comment: 11 page

Handheld-Impedance-Measurement System with seven-decade capability and potentiostatic function

This paper describes design and test of a new impedance-measurement system for nonlinear devices that exhibits a seven-decade range and works down to a frequency of 0.01 Hz. The system is specifically designed for electrochemical measurements, but the proposed architecture can be employed in many other fields where flexible signal generation and analysis are required. The system employs an unconventional signal generator based on two pulsewidth modulation (PWM) oscillators and an autocalibration system that allows uncertainties of less than 3% to be obtained over a range of 1 kΩ to 100 GΩ. A synchronous demodulation processing allows the noise superimposed to the low-amplitude input signals to be made negligibl

Evolutionary context improves regulatory network predictions

A novel algorithm harnesses phylogenetic information and facilitates a better understanding of the evolutionary divergence of gene regulation between species

Glycerol as high-permittivity liquid filler in dielectric silicone elastomers

A recently reported novel class of elastomers was tested with respect to its dielectric properties. The new elastomer material is based on a commercially available poly(dimethylsiloxane) composition, which has been modified by embedding glycerol droplets into its matrix. The approach has two major advantages that make the material useful in a dielectric actuator. First, the glycerol droplets efficiently enhance the dielectric constant, which can reach astonishingly high values in the composite. Second, the liquid filler also acts as a softener that effectively decreases the elastic modulus of the composite. In combination with very low cost and easy preparation, the two property enhancements lead to an extremely attractive dielectric elastomer material. Experimental permittivity data are compared to various theoretical models that predict relative permittivity changes as a function of filler loading, and the applicability of the models is discussed. (c) 2016 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2016, 133, 44153

Origins, evolution, domestication and diversity of Saccharomyces beer yeasts

Yeasts have been used for food and beverage fermentations for thousands of years. Today, numerous different strains are available for each specific fermentation process. However, the nature and extent of the phenotypic and genetic diversity and specific adaptations to industrial niches have only begun to be elucidated recently. In Saccharomyces, domestication is most pronounced in beer strains, likely because they continuously live in their industrial niche, allowing only limited genetic admixture with wild stocks and minimal contact with natural environments. As a result, beer yeast genomes show complex patterns of domestication and divergence, making both ale (S. cerevisiae) and lager (S. pastorianus) producing strains ideal models to study domestication and, more generally, genetic mechanisms underlying swift adaptation to new niches