Solvable Cubic Resonant Systems

On Cubic Graphs Admitting an Edge-Transitive Solvable Group

Using covering graph techniques, a structural result about connected cubic simple graphs admitting an edge-transitive solvable group of automorphisms is proved. This implies, among other, that every such graph can be obtained from either the 3-dipole Dip3 or the complete graph K4, by a sequence of elementary-abelian covers. Another consequence of the main structural result is that the action of...

Resonant Raman scattering in cubic and hexagonal boron nitride

We measured firstand second-order Raman scattering in cubic and hexagonal boron nitride using excitation energies in the visible and in the UV. The nonresonant first-order Raman susceptibilities for cubic and hexagonal BN are 1 and 10 Å2, respectively. Raman scattering is thus very powerful in detecting the hexagonal phase in mixed thin boron nitride films. In cubic BN the constant Raman sucsep...

Electron transport through cubic InGaN/AlGaN resonant tunneling diodes

We theoretically study the electron transport through a resonant tunneling diode (RTD) based on strained AlxGa1−xN/In0.1Ga0.9N/AlxGa1−xN quantumwells embedded in relaxed n-Al0.15Ga0.85N/strained In0.1Ga0.9N emitter and collector. The aluminum composition in both injector and collector contacts is taken relatively weak; this does not preclude achieving a wide band offset at the border of the pre...

Quasi-Exactly Solvable Systems and Orthogonal Polynomials

This paper shows that there is a correspondence between quasi-exactly solvable models in quantum mechanics and sets of orthogonal polynomials {Pn}. The quantum-mechanical wave function is the generating function for the Pn(E), which are polynomials in the energy E. The condition of quasi-exact solvability is reflected in the vanishing of the norm of all polynomials whose index n exceeds a criti...

Edge-colourings of cubic graphs admitting a solvable vertex-transitive group of automorphisms