Relativistic shape invariant potentials

Dirac equation for a charged spinor in electromagnetic field is written for special cases of spherically symmetric potentials. This facilitates the introduction of relativistic extensions of shape invariant potential classes. We obtain the relativistic spectra and spinor wavefunctions for all potentials in one of these classes. The nonrelativistic limit reproduces the usual Rosen-Morse I & II, Eckart, Poschl-Teller, and Scarf potentials.Comment: Corrigendum: The last statement above equation (1) is now corrected and replaced by two new statement

New Shape Invariant Potentials in Supersymmetric Quantum Mechanics

Quantum mechanical potentials satisfying the property of shape invariance are well known to be algebraically solvable. Using a scaling ansatz for the change of parameters, we obtain a large class of new shape invariant potentials which are reflectionless and possess an infinite number of bound states. They can be viewed as q-deformations of the single soliton solution corresponding to the Rosen-Morse potential. Explicit expressions for energy eigenvalues, eigenfunctions and transmission coefficients are given. Included in our potentials as a special case is the self-similar potential recently discussed by Shabat and Spiridonov.Comment: 8pages, Te

Ballistic deposition patterns beneath a growing KPZ interface

We consider a (1+1)-dimensional ballistic deposition process with next-nearest neighbor interaction, which belongs to the KPZ universality class, and introduce for this discrete model a variational formulation similar to that for the randomly forced continuous Burgers equation. This allows to identify the characteristic structures in the bulk of a growing aggregate ("clusters" and "crevices") with minimizers and shocks in the Burgers turbulence, and to introduce a new kind of equipped Airy process for ballistic growth. We dub it the "hairy Airy process" and investigate its statistics numerically. We also identify scaling laws that characterize the ballistic deposition patterns in the bulk: the law of "thinning" of the forest of clusters with increasing height, the law of transversal fluctuations of cluster boundaries, and the size distribution of clusters. The corresponding critical exponents are determined exactly based on the analogy with the Burgers turbulence and simple scaling considerations.Comment: 10 pages, 5 figures. Minor edits: typo corrected, added explanation of two acronyms. The text is essentially equivalent to version

A search on Dirac equation

The solutions, in terms of orthogonal polynomials, of Dirac equation with analytically solvable potentials are investigated within a novel formalism by transforming the relativistic equation into a Schrodinger like one. Earlier results are discussed in a unified framework and certain solutions of a large class of potentials are given.Comment: 9 page

PGC-1α controls mitochondrial biogenesis and dynamics in lead-induced neurotoxicity

Due to its role in regulation of mitochondrial function, PGC1α is emerging as an important player in ageing and neurodegenerative disorders. PGC1α exerts its neuroprotective effects by promoting mitochondrial biogenesis (MB) and functioning. However, the precise regulatory role of PGC1α in the control of mitochondrial dynamics (MD) and neurotoxicity is still unknown. Here we elucidate the role of PGC1α in vitro and in vivo in the regulatory context of MB and MD in response to lead (II) acetate as a relevant model of neurotoxicity. We show that there is an adaptive response (AR) to lead, orchestrated by the BAP31-calcium signalling system operating between the ER and mitochondria. We find that this hormetic response is controlled by a cell-tolerated increase of PGC1α expression, which in turn induces a balanced expression of fusion/fission genes by binding to their promoters and implying its direct role in regulation of MD. However, dysregulation of PGC1α expression through either stable downregulation or overexpression, renders cells more susceptible to lead insult leading to mitochondrial fragmentation and cell death. Our data provide novel evidence that PGC1α expression is a key regulator of MD and the maintenance of tolerated PGC1α expression may offer a promising strategy for neuroprotective therapies.España Ministerio de Economía y Competitividad SAF2012-3902

Quantum switches and quantum memories for matter-wave lattice solitons

We study the possibility of implementing a quantum switch and a quantum memory for matter wave lattice solitons by making them interact with "effective" potentials (barrier/well) corresponding to defects of the optical lattice. In the case of interaction with an "effective" potential barrier, the bright lattice soliton experiences an abrupt transition from complete transmission to complete reflection (quantum switch) for a critical height of the barrier. The trapping of the soliton in an "effective" potential well and its release on demand, without loses, shows the feasibility of using the system as a quantum memory. The inclusion of defects as a way of controlling the interactions between two solitons is also reported

Mapping of shape invariant potentials by the point canonical transformation

In this paper by using the method of point canonical transformation we find that the Coulomb and Kratzer potentials can be mapped to the Morse potential. Then we show that the P\"{o}schl-Teller potential type I belongs to the same subclass of shape invariant potentials as Hulth\'{e}n potential. Also we show that the shape-invariant algebra for Coulomb, Kratzer, and Morse potentials is SU(1,1), while the shape-invariant algebra for P\"{o}schl-Teller type I and Hulth\'{e}n is SU(2)

Unintended consequences of drug policies experienced by young drug users in contact with the criminal justice systems

The aim of this paper is to assess to what extent prohibitive drug policies hamper the management of drug problems from the perspective of young people who have experience with the criminal justice systems (CJS). Qualitative, in-depth interviews were carried out in six European countries (Austria, Denmark, Germany, Italy, Poland, and the UK) following a common interview guide to obtain comparative data on the life trajectories of drug experienced youth. Altogether 198 interviews with people aged 14–25 years were collected and analysed by national teams following a common coding book. Unintended consequences of drug policies for the individual and society were identified. Individual consequences included health consequences and traumatic experiences with law enforcement. Social consequences included those affecting social relations such as stigmatisation and those impacting on institutions, for example, focusing on drug use and neglecting other problems. This paper confirmed earlier research indicating unintended consequences of prohibitive drug policies but also added to the literature its cross-national perspective and use of young people narratives as a source of analyses. There are, however, policy measures available that may reduce the volume and range of unintended effects. Their implementation is crucial to reduce the array of unintended consequences of prohibitive drug policies