Automorphisms of the q-oscillator algebra and basic orthogonal polynomials

Certain automorphisms of the quantum oscillator algebra are shown to provide an algebraic interpretation for q-generalizations of the Charlier polynomials.     

Acidic and reductive dissolution of magnetite in aqueous sulfuric acid: Site-binding model and experimental results

The open circuit dissolution of ionic metal oxides in mineral acids is modelled assuming that the rate is controlled by the transfer of metal ions in hydrolytic equilibrium with bulk metal ions, from the metal oxide surface to the Stern plane. The site-binding model of the double layer metal oxide/electrolyte solution is used to obtain the pH dependence of surface and Stern potentials. The nature of the active sites is discussed and their surface concentration is assumed to be proportional to suface charge σ₀. Again, the site-binding model is used to detemine the pH dependence of σ₀. It is thus shown that the rate order in c_H⁺ is essentially defined by the potential dependence of the charge transfer process, for oxides with points of zero charge near neutrality that dissolve in mildly or strongly acidic solutions. The role of surface complexation is also discussed in terms of the site-binding model and the difficulties in interpreting dissolution experiments under constant external applied potential are discussed in terms of the complexity of the semiconductor oxide/electrolyte solution interfacial region in magnetite.An experimental study of the open circuit dissolution of magnetite in sulfuric acid is presented and interpreted according to the proposed model.The reductive dissolution of magnetite is modelled by extension of the Valverde-Wagner model of oxide dissolution. Experimental results are presented to demonstrate that the reductive dissolution rate of magnetite in ferrous containing solutions is controlled by the rate of electron transfer from adsorbed Fe(II) to Fe(III) surface states of magnetite.     

On a bosonic-parafermionic realization ofU_q (\widehat{sl(2)})

We realize the current algebra at an arbitrary level in terms of one deformed free bosonic field and a pair of deformed parafermionic fields. It is shown that the operator product expansions of these parafermionic fields involve an infinite number of simple poles and simple zeros, which then condensate to form a branch cut in the classical limitq1. Our realization coincides with those of Frenkel-Jing and Bernard when the levelk takes the values 1 and 2, respectively.     

Symmetries of the heat equation on the lattice

Discrete versions of the heat equation on two-dimensional uniform lattices are shown to possess the same symmetry algebra as their continuum limits. Solutions with definite symmetry properties are presented.     

An algebraic interpretation of the multivariate <Emphasis Type="Italic">q</Emphasis>-Krawtchouk polynomials

The multivariate quantum q-Krawtchouk polynomials are shown to arise as matrix elements of “q-rotations” acting on the state vectors of many q-oscillators. The focus is put on the two-variable case. The algebraic interpretation is used to derive the main properties of the polynomials: orthogonality, duality, structure relations, difference equations, and recurrence relations. The extension to an arbitrary number of variables is presented.     

Individual charge traps in silicon nanowires

We study anomalies in the Coulomb blockade spectrum of a quantum dot formed in a silicon nanowire. These anomalies are attributed to electrostatic interaction with charge traps in the device. A simple model reproduces these anomalies accurately and we show how the capacitance matrices of the traps can be obtained from the shape of the anomalies. From these capacitance matrices we deduce that the traps are located near or inside the wire. Based on the occurrence of the anomalies in wires with different doping levels we infer that most of the traps are arsenic dopant states. In some cases the anomalies are accompanied by a random telegraph signal which allows time resolved monitoring of the occupation of the trap. The spin of the trap states is determined via the Zeeman shift.     

Two-Dimensional Krall–Sheffer Polynomials andQuantum Systems on Spaces with Constant Curvature

Krall and Sheffer found in 1967 that there exists at most nine different types of two-dimensional orthogonal polynomials which are eigensolutions of a second-order linear differential operator with polynomial coefficients. We show that, for all these types, there correspond quantum mechanical systems on a Euclidean (pseudo-Eeuclidean) plane, two-dimensional sphere, or hyperboloid.     

Creation Operators for the Macdonald and Jack Polynomials

Formulas of Rodrigues-type for the Macdonald polynomials are presented. They involve creation operators, certain properties of which are proved and other conjectured. The limiting case of the Jack polynomials is discussed.