A superintegrable finite oscillator in two dimensions with SU(2) symmetry

A superintegrable finite model of the quantum isotropic oscillator in two dimensions is introduced. It is defined on a uniform lattice of triangular shape. The constants of the motion for the model form an SU(2) symmetry algebra. It is found that the dynamical difference eigenvalue equation can be written in terms of creation and annihilation operators. The wavefunctions of the Hamiltonian are expressed in terms of two known families of bivariate Krawtchouk polynomials; those of Rahman and those of Tratnik. These polynomials form bases for SU(2) irreducible representations. It is further shown that the pair of eigenvalue equations for each of these families are related to each other by an SU(2) automorphism. A finite model of the anisotropic oscillator that has wavefunctions expressed in terms of the same Rahman polynomials is also introduced. In the continuum limit, when the number of grid points goes to infinity, standard two-dimensional harmonic oscillators are obtained. The analysis provides the $N\rightarrow \infty$ limit of the bivariate Krawtchouk polynomials as a product of one-variable Hermite polynomials

Quantum state transfer in spin chains with q-deformed interaction terms

We study the time evolution of a single spin excitation state in certain linear spin chains, as a model for quantum communication. Some years ago it was discovered that when the spin chain data (the nearest neighbour interaction strengths and the magnetic field strengths) are related to the Jacobi matrix entries of Krawtchouk polynomials or dual Hahn polynomials, so-called perfect state transfer takes place. The extension of these ideas to other types of discrete orthogonal polynomials did not lead to new models with perfect state transfer, but did allow more insight in the general computation of the correlation function. In the present paper, we extend the study to discrete orthogonal polynomials of q-hypergeometric type. A remarkable result is a new analytic model where perfect state transfer is achieved: this is when the spin chain data are related to the Jacobi matrix of q-Krawtchouk polynomials. The other cases studied here (affine q-Krawtchouk polynomials, quantum q-Krawtchouk polynomials, dual q-Krawtchouk polynomials, q-Hahn polynomials, dual q-Hahn polynomials and q-Racah polynomials) do not give rise to models with perfect state transfer. However, the computation of the correlation function itself is quite interesting, leading to advanced q-series manipulations

Nanostructured Cu2ZnSnS4 Thin Films on Porous-Si Wafer

 Nanostructure CZTS thin film was fabricated by electrodeposition technique. To manufacture the heterojunctions, p-type c-Si wafers of (100) orientation were used as a substrate.  Before anodization, the surface of the c-Si substrates were etched in an aqueous solution of HF and further washed in distilled water (at temperature of 80°С and ethyl alcohol and then dried in air. The current-voltage characteristics of the CZTS /PS solar cell under dark conditions show that forward bias current variation approximately exponentially with voltage bias. The capacitance for Nano- CZTS /PS Solar Cell decreases with the increase of the reverse bias voltage and with the increasing of etching time of nPS layers. That heterojunctions demonstrate good photo-response in the wavelength range of 510 - 650 nm

The Wigner distribution function for the one-dimensional parabose oscillator

In the beginning of the 1950's, Wigner introduced a fundamental deformation from the canonical quantum mechanical harmonic oscillator, which is nowadays sometimes called a Wigner quantum oscillator or a parabose oscillator. Also, in quantum mechanics the so-called Wigner distribution is considered to be the closest quantum analogue of the classical probability distribution over the phase space. In this article, we consider which definition for such distribution function could be used in the case of non-canonical quantum mechanics. We then explicitly compute two different expressions for this distribution function for the case of the parabose oscillator. Both expressions turn out to be multiple sums involving (generalized) Laguerre polynomials. Plots then show that the Wigner distribution function for the ground state of the parabose oscillator is similar in behaviour to the Wigner distribution function of the first excited state of the canonical quantum oscillator.Comment: 20 pages, 2 EPS figures, published in Journal of Physics

Safety and Availability of Clofazimine in the Treatment of Multidrug and Extensively Drug-Resistant Tuberculosis: Analysis of Published Guidance and Meta-Analysis of Cohort Studies

Objectives: Given the spread of multidrug-resistant tuberculosis (MDR-TB), new therapies are urgently needed, including the repurposing of existing drugs. We aimed to assess key considerations for the clinical and programmatic use of clofazimine (Cfz), a riminophenazine with anti-mycobacterial activity currently used to treat leprosy. Design: Fixed and random effects meta-analysis of cohort studies and systematic review Setting: Electronic and manual searches were combined. Inclusion criteria: Observational studies on treatment of multidrug- and extremely drug- resistant tuberculosis with clofazimine or a clofazimine-containing regimen, and published guidance and documents relating to cost and availability were eligible. Results: Five observational studies enrolled 861 patients, of which 602 received Cfz. The pooled proportion of adverse drug reactions requiring discontinuation of Cfz treatment was 0.1% (95% CI: [0.0, 0.6%]), and the median frequency of all adverse events was 5.1%. Cfz showed in vitro efficacy against Mycobacterium tuberculosis, and Cfz-containing regimens may have had a useful role in the treatment of patients with drug-resistant strains and who had limited alternative treatment options. However, Cfz uptake remains insufficient to meet global needs; there is only one internationally quality-assured manufacturer, which produces a limited quantity of the drug prioritised for treatment of leprosy, the only indication for which the drug is registered. Conclusions: While the data were limited, Cfz was associated with a risk for adverse drug reactions comparable to that of first-line TB treatment, which could be reasonably managed under programmatic conditions. However, low market availability and high cost are important barriers to access to Cfz for MDR-TB patients.Other Research Uni

A relativistic model of the NN-dimensional singular oscillator

Exactly solvable $N$-dimensional model of the quantum isotropic singular oscillator in the relativistic configurational $\vec r_N$-space is proposed. It is shown that through the simple substitutions the finite-difference equation for the $N$-dimensional singular oscillator can be reduced to the similar finite-difference equation for the relativistic isotropic three-dimensional singular oscillator. We have found the radial wavefunctions and energy spectrum of the problem and constructed a dynamical symmetry algebra.Comment: 8 pages, accepted for publication in J. Phys.

On the Wigner function of the relativistic finite-difference oscillator in an external field

The phase-space representation for a relativistic linear oscillator in a homogeneous external field expressed through the finite-difference equation is constructed. Explicit expressions of the relativistic oscillator Wigner quasi-distribution function for the stationary states as well as of states of thermodynamical equilibrium are obtained and their correct limits are shown.Comment: 12 pages, 6 figures, IOP styled LaTeX, to be published in Journal of Physics

An infinite family of superintegrable Hamiltonians with reflection in the plane

We introduce a new infinite class of superintegrable quantum systems in the plane. Their Hamiltonians involve reflection operators. The associated Schr\"odinger equations admit separation of variables in polar coordinates and are exactly solvable. The angular part of the wave function is expressed in terms of little -1 Jacobi polynomials. The spectra exhibit "accidental" degeneracies. The superintegrability of the model is proved using the recurrence relation approach. The (higher-order) constants of motion are constructed and the structure equations of the symmetry algebra obtained.Comment: 19 page

The Relativistic Linear Singular Oscillator

Exactly-solvable model of the linear singular oscillator in the relativistic configurational space is considered. We have found wavefunctions and energy spectrum for the model under study. It is shown that they have correct non-relativistic limits.Comment: 14 pages, 12 figures in eps format, IOP style LaTeX file (revised taking into account referees suggestions

Finite oscillator models: the Hahn oscillator

A new model for the finite one-dimensional harmonic oscillator is proposed based upon the algebra u(2)_{\alpha}. This algebra is a deformation of the Lie algebra u(2) extended by a parity operator, with deformation parameter {\alpha}. A class of irreducible unitary representations of u(2)_{\alpha} is constructed. In the finite oscillator model, the (discrete) spectrum of the position operator is determined, and the position wave functions are shown to be dual Hahn polynomials. Plots of these discrete wave functions display interesting properties, similar to those of the parabose oscillator. We show indeed that in the limit, when the dimension of the representations goes to infinity, the discrete wave functions tend to the continuous wave functions of the parabose oscillator