Variations on the Planar Landau Problem: Canonical Transformations, A Purely Linear Potential and the Half-Plane

The ordinary Landau problem of a charged particle in a plane subjected to a perpendicular homogeneous and static magnetic field is reconsidered from different points of view. The role of phase space canonical transformations and their relation to a choice of gauge in the solution of the problem is addressed. The Landau problem is then extended to different contexts, in particular the singular situation of a purely linear potential term being added as an interaction, for which a complete purely algebraic solution is presented. This solution is then exploited to solve this same singular Landau problem in the half-plane, with as motivation the potential relevance of such a geometry for quantum Hall measurements in the presence of an electric field or a gravitational quantum well

Influence of a Point-to-Plane DC Negative Corona Discharge on Gel Surfaces

Point-to-plane corona discharge is widely used for modifying polymer surfaces for biomedical applications and for sterilization and decontamination. This paper focuses on an experimental investigation of the influence of the single-point and multi-point corona discharge electric field on gel surface. Three types of gelatinous agar were used as the gel medium: blood agar, nutrient agar and Endo agar. The gel surface modification was studied for various time periods and discharge currents.

An Unfolded Quantization for Twisted Hopf Algebras

In this talk I discuss a recently developed "Unfolded Quantization Framework". It allows to introduce a Hamiltonian Second Quantization based on a Hopf algebra endowed with a coproduct satisfying, for the Hamiltonian, the physical requirement of being a primitive element. The scheme can be applied to theories deformed via a Drinfeld twist. I discuss in particular two cases: the abelian twist deformation of a rotationally invariant nonrelativistic Quantum Mechanics (the twist induces a standard noncommutativity) and the Jordanian twist of the harmonic oscillator. In the latter case the twist induces a Snyder non-commutativity for the space-coordinates, with a pseudo-Hermitian deformed Hamiltonian. The "Unfolded Quantization Framework" unambiguously fixes the non-additive effective interactions in the multi-particle sector of the deformed quantum theory. The statistics of the particles is preserved even in the presence of a deformation.Comment: 9 pages. Talk given at QTS7 (7th Int. Conf. on Quantum Theory and Symmetries, Prague, August 2011

Corona discharge influence on micro-organisms

It is known, that the electric discharge can be used for micro-organism killing. Presented paper describes first qualitative results of atmospheric corona discharge influence on moulds (penicillium digitatum) experimental study. It seems, that the atmospheric corona discharge inhibits the fungi growth only. It seems, it does not kill both the living organism of mould and the spores. Preliminary experimental results indicate, that the ozone generated by atmospheric corona dicharge does not influence the fungi, too.Відомо, що електричний розряд може бути використаний для знищення мікроорганізмів. В роботі, що надається, описані перші якісні результати експериментального дослідження впливу атмосферного коронного розряду на плісеневий грибок (penicillium digitatum). Здається, що коронний розряд лише перешкоджає зросту грибків, але не вбиває ані організм плісені, що живе, ані її спори. Попередні результати експерименту вказують, що озон, який генерується атмосферним коронним розрядом , також не впливає на грибки.Известно, что электрический разряд можно использовать для уничтожения микроорганизмов. В представленной работе описаны первые качественные результаты экспериментального исследования влияния атмосферного коронного разряда на плесенный грибок (penicillium digitatum). Представляется, что коронный разряд лишь препятствует росту грибков, но не убивает ни живущий организм плесени, ни её споры. Предварительные результаты эксперимента показывают, что озон, который генерируется атмосферным коронным разрядом, также не влияет на грибки

Quasi-Hermitian supersymmetric extensions of a non-Hermitian oscillator Hamiltonian and of its generalizations

A harmonic oscillator Hamiltonian augmented by a non-Hermitian \pt-symmetric part and its su(1,1) generalizations, for which a family of positive-definite metric operators was recently constructed, are re-examined in a supersymmetric context. Quasi-Hermitian supersymmetric extensions of such Hamiltonians are proposed by enlarging su(1,1) to a ${\rm su}(1,1/1) \sim {\rm osp}(2/2, \R)$ superalgebra. This allows the construction of new non-Hermitian Hamiltonians related by similarity to Hermitian ones. Some examples of them are reviewed.Comment: 15 pages, no figure; published versio

Bosonization in d=2 from finite chiral determinants with a Gauss decomposition

We show how to bosonize two-dimensional non-abelian models using finite chiral determinants calculated from a Gauss decomposition. The calculation is quite straightforward and hardly more involved than for the abelian case. In particular, the counterterm $A\bar A$, which is normally motivated from gauge invariance and then added by hand, appears naturally in this approach.Comment: 4 pages, Revte

Moyal products -- a new perspective on quasi-hermitian quantum mechanics

The rationale for introducing non-hermitian Hamiltonians and other observables is reviewed and open issues identified. We present a new approach based on Moyal products to compute the metric for quasi-hermitian systems. This approach is not only an efficient method of computation, but also suggests a new perspective on quasi-hermitian quantum mechanics which invites further exploration. In particular, we present some first results which link the Berry connection and curvature to non-perturbative properties and the metric.Comment: 14 pages. Submitted to J Phys A special issue on The Physics of Non-Hermitian Operator

Voros product and the Pauli principle at low energies

Using the Voros star product, we investigate the status of the two particle correlation function to study the possible extent to which the previously proposed violation of the Pauli principle may impact at low energies. The results show interesting features which are not present in the computations made using the Moyal star product.Comment: 5 pages LateX, minor correction