We study electron energies in a double concentric quantum ring with anisotropy in the rims heights in the presence of the external magnetic field applied along the symmetry axis. To this end, we consider a model in which the thickness grows linearly from the axis up to the inner rim with a slope different from one between the inner and the outer rims. The anisotropy in the rims heights originated by the presence in the structure of various valleys we simulate by periodic dependence of the slope on the radial direction. We show that the wave functions of the electron confined in such structure can be found analytically if the slopes in all radial directions are the same, and by using a simple exact diagonalization procedure otherwise. The behavior of the electron energies as functions of the magnetic field, rings radii and rims heights, as well as the number of the valleys and their depths is consistently described with our formalism. The entanglement of the states with different radial and orbital quantum numbers, the period and the amplitude of the Aharonov–Bohm oscillations are very sensible to any variations of the rims heights. 相似文献
Let R be a prime ring, L a noncentral Lie ideal and σ a nontrivial automorphism of R such that usσ(u)ut= 0 for all u ∈ L, where s, t are fixed non-negative integers. If either char R s + t or char R = 0, then R satisfies s4, the standard identity in four variables. We also examine the identity(σ([x, y])-[x, y])n=0 for all x, y ∈ I, where I is a nonzero ideal of R and n is a fixed positive integer. If either char R n or char R = 0, then R is commutative. 相似文献
Today's olefin metathesis catalysts show high reactivity, selectivity, and functional group tolerance and allow the design of new syntheses of precisely functionalized polymers. Here the synthesis of a new end‐capping reagent is investigated allowing the introduction of a highly reactive activated ester end‐group at the polymer chain end as well as its prefunctionalization to directly introduce functional moieties. The versatility of this new end‐capping reagent is demonstrated by utilizing it to synthesize a so‐called termimer (a monomer with termination capabilities). Copolymerization of a norbornene derivative with the termimer leads to hyperbranched ring‐opening metathesis polymerization polymers as proven by gel permeation chromatography and MALDI‐ToF‐(matrix‐assisted laser desorption/ionization time of flight) mass spectrometry.
