We develop a method of reducing the size of quantum minors in the algebra of quantum matrices Oq(Mn). We use the method to show that the quantum determinantal factor rings of Oq(Mn(C)) are maximal orders, for q an element of C transcendental over Q. 2000 Mathematics subject classification: 16P40, 16W35, 20G42.

We study the e ect of spin-orbit iteration on the electron energy spectra in tree-dimensional (3D) nanoscale semiconductor quantum rings. Ultrasmall InAs quantum ring embedded in GaAs matrix is numerically solved with the e ective one electronic band Hamiltonian, the energyand position-dependent electron e ective mass approximation, and the spin-dependent Ben Daniel-Duke boundary conditions. Th...

Molecular beam epitaxy of InAs/GaAs quantum dots and their subsequent transformation to quantum rings by postepitaxy thermal annealing have been investigated. Photoconductive detectors with multiple quantum ring layers in the active region exhibit dark current density 10−8 A /cm2 at a bias of 2 V at 4.2 K. The rings have a single bound state, and emission of photoexcited carriers gives rise to ...

In this work we report on the ability to form low density Ga(As)Sb quantum ring-shaped nanostructures (Q-rings) on GaAs(001) substrates by the droplet epitaxy technique. The Q-rings are formed by crystallization of Ga droplets under antimony flux. After being capped by a GaAs layer, these nanostructures show surface mounding features that are correlated with the buried nanostructures, as demons...

The notion of quantum cohomology was first proposed by Witten [Va, Wi], based on topological field theory. Its mathematical theory was only established recently by Y. Ruan and the second named author [RT, Ru], where they proved the existence of the quantum rings on semi-positive symplectic manifolds. (Fano manifolds are particular semi-positive manifolds.) In this note, we will provide a purely...

One-dimensional and two-dimensional conductivity calculations are done for a set of several closely spaced quantum silicon rings, following the development of bottom-up approaches for producing silicon rings. The transmission is easily influenced by electric and magnetic gatings and has band features even for two or three rings, showing its potential usefulness for logical devices. Analysis on ...

We study weak localization in chains of metallic rings. We show than nonlocality of quantum transport can drastically affect the behaviour of the harmonics of magnetoconductance oscillations. Two different geometries are considered : the case of rings separated by long wires compared to the phase coherence length and the case of contacted rings. In a second part we discuss the role of decoheren...

We study deformations of cluster algebras with several quantum parameters, called toroidal algebras, which naturally appear in the Grothendieck rings representations affine algebras. In this context, we construct and establish these are flat rings. prove that for a family monoidal categories $${\mathscr {C}}_1$$ simply-laced categorifying finite-type ring has natural structure algebra.

in this study, the role of interaction of pi electrons on the strength of simultaneous σ-hole interactions (pnicogen, chalcogen and halogen bonds) is investigated using the quantum chemical calculations. x-ben||taz∙∙∙y1,y2,y3 complexes (x = cn, f, cl, br, ch3 , oh and nh2, taz= s-triazine and y1,y2 and y3 denotes ph2f, hsf, and clf molecules) is introduced as a model. the results show that inte...