82 research outputs found
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 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
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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 -dimensional singular oscillator
Exactly solvable -dimensional model of the quantum isotropic singular
oscillator in the relativistic configurational -space is proposed. It
is shown that through the simple substitutions the finite-difference equation
for the -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
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