On the κ\kappa-Dirac Oscillator revisited

This Letter is based on the $\kappa$-Dirac equation, derived from the $\kappa$-Poincar\'{e}-Hopf algebra. It is shown that the $\kappa$-Dirac equation preserves parity while breaks charge conjugation and time reversal symmetries. Introducing the Dirac oscillator prescription, $\mathbf{p}\to\mathbf{p}-im\omega\beta\mathbf{r}$, in the $\kappa$-Dirac equation, one obtains the $\kappa$-Dirac oscillator. Using a decomposition in terms of spin angular functions, one achieves the deformed radial equations, with the associated deformed energy eigenvalues and eigenfunctions. The deformation parameter breaks the infinite degeneracy of the Dirac oscillator. In the case where $\varepsilon=0$, one recovers the energy eigenvalues and eigenfunctions of the Dirac oscillator.Comment: 5 pages, no figures, accepted for publication in Physics Letters

Effects of quantum deformation on the spin-1/2 Aharonov-Bohm problem

In this letter we study the Aharonov-Bohm problem for a spin-1/2 particle in the quantum deformed framework generated by the $\kappa$-Poincar\'{e}-Hopf algebra. We consider the nonrelativistic limit of the $\kappa$-deformed Dirac equation and use the spin-dependent term to impose an upper bound on the magnitude of the deformation parameter $\varepsilon$. By using the self-adjoint extension approach, we examine the scattering and bound state scenarios. After obtaining the scattering phase shift and the $S$-matrix, the bound states energies are obtained by analyzing the pole structure of the latter. Using a recently developed general regularization prescription [Phys. Rev. D. \textbf{85}, 041701(R) (2012)], the self-adjoint extension parameter is determined in terms of the physics of the problem. For last, we analyze the problem of helicity conservation.Comment: 12 pages, no figures, submitted for publicatio

Remarks on the Aharonov-Casher dynamics in a CPT-odd Lorentz-violating background

The Aharonov-Casher problem in the presence of a Lorentz-violating background nonminimally coupled to a spinor and a gauge field is examined. Using an approach based on the self-adjoint extension method, an expression for the bound state energies is obtained in terms of the physics of the problem by determining the self-adjoint extension parameter.Comment: Matches published versio

Safety of herbal medicinal products: Echinacea and selected alkylamides do not induce CYP3A4 mRNA expression

Copyright © 2011 Maryam Modarai et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.A major safety concern with the use of herbal medicinal products (HMP) is their interactions with conventional medicines, which are often mediated via the cytochrome P450 (CYP) system. Echinacea is a widely used over-the-counter HMP, with proven immunomodulatory properties. Its increasing use makes research into its safety an urgent concern. Previously, we showed that Echinacea extracts and its alkylamides (thought to be important for Echinacea's immunomodulatory activity) mildly inhibit the enzymatic activity of the main drug metabolising CYP isoforms, but to this date, there is insufficient work on its ability to alter CYP expression levels. We now report for the first time the effect of a commercial Echinacea extract (Echinaforce) and four Echinacea alkylamides on the transcription of the major drug metabolizing enzyme CYP3A4. HepG2 cells were exposed for 96 h to clinically relevant concentrations of Echinaforce (22, 11.6 and 1.16g mL-1) or the alkylamides (1.62 and 44 nM). CYP3A4 mRNA levels were quantified using real-time reverse transcription polymerase chain reaction (RT-PCR). Neither Echinaforce nor the alkylamides produced any significant changes in the steady-state CYP3A4 mRNA levels, under these conditions. In contrast, treatment with 50M rifampicin resulted in a 3.8-fold up-regulation over the vehicle control. We conclude that Echinaforce is unlikely to affect CYP3A4 transcriptional levels, even at concentrations which can inhibit the enzymatic activity of CYP3A4. Overall, our data provides further evidence for the lack of interactions between Echinacea and conventional drugs.Bioforce, Switzerland and the Maplethorpe Trust (University of London)

Thermodynamic Formalism for Topological Markov Chains on Borel Standard Spaces

We develop a Thermodynamic Formalism for bounded continuous potentials defined on the sequence space $X\equiv E^{\mathbb{N}}$, where $E$ is a general Borel standard space. In particular, we introduce meaningful concepts of entropy and pressure for shifts acting on $X$ and obtain the existence of equilibrium states as additive probability measures for any bounded continuous potential. Furthermore, we establish convexity and other structural properties of the set of equilibrium states, prove a version of the Perron-Frobenius-Ruelle theorem under additional assumptions on the regularity of the potential and show that the Yosida-Hewitt decomposition of these equilibrium states do not have a purely additive part. We then apply our results to the construction of invariant measures of time-homogeneous Markov chains taking values on a general Borel standard space and obtain exponential asymptotic stability for a class of Markov operators. We also construct conformal measures for an infinite collection of interacting random paths which are associated to a potential depending on infinitely many coordinates. Under an additional differentiability hypothesis, we show how this process is related after a proper scaling limit to a certain infinite dimensional diffusion.Comment: Accepted for publication in Discrete and Continuous Dynamical Systems. 23 page