We describe the small quantum cohomology ring of complete flag varieties by algebro-geometric methods, as presented in our previous work Quantum cohomology of flag varieties (Internat. Math. Res. Notices, no. 6 (1995), 263–277). We also give a geometric proof of the quantum Monk formula.

Ring-like quantum structures generalizing Boolean rings and having the property that the terms corresponding to the two normal forms of the symmetric difference in Boolean algebras coincide are investigated. Subclasses of these structures are algebraically characterized and related to quantum logic. In particular, a physical interpretation of the proposed model following Mackey’s approach to ax...

stability of the π-π stacking interactions in the ben||substituted-coronene and hfben||substituted-coronene complexes was studied using the computational quantum chemistry methods (where ben and hfben are benzene and hexaflourobenzene, || denotes π-π stacking interaction, substituted-coronene is coronene molecule which substituted with four x groups, and x= nh2, ch3, oh, h, f, cf3, cn and no). ...

The spectra of quantum dots of different geometry (" quantum ring " , " quantum cylinder " , " spherical square-well " and " parabolic ") are studied. The stochastic variational method on correlated Gaussian basis functions and a large scale shell-model approach have been used to investigate these " artificial " atoms and their properties in magnetic field. Accurate numerical results are presen...

We find presentations by generators and relations for the equivariant quantum cohomology of the Grassmannian. For these presentations, we also find determinantal formulae for the equivariant quantum Schubert classes. To prove this, we use the theory of factorial Schur functions and a characterization of the equivariant quantum cohomology ring.

in this paper, we study the electronic properties of a concentric triple quantum ring using exact diagonalization technique. the energy spectra and magnetization for a single electron and two electrons, in the presence of an applied magnetic field, are calculated and discussed. it is shown that, for two-interacting electrons, the period of aharonov-bohm oscillations decreases to the half of tha...

In this paper, we study the (small) quantum cohomology ring of the partial flag manifold. We give proofs of the presentation of the ring and of the quantum Giambelli formula for Schubert varieties. These are known results, but our proofs are more natural and direct than the previous ones. One of our goals is to give evidence of a relationship between universal Schubert polynomials, which give t...

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...

in this paper, we study some ring theoretic properties of the amalgamated duplication ring $rbowtie i$ of a commutative noetherian ring $r$ along an ideal $i$ of $r$ which was introduced by d'anna and fontana. indeed, it is determined that when $rbowtie i$ satisfies serre's conditions $(r_n)$ and $(s_n)$, and when is a normal ring, a generalized cohen-macaulay ring and finally a filter ring.

To improve the photophysical performance of colloidal quantum dots for laser applications, sophisticated core/shell geometries have been developed. Typically, a wider bandgap semiconductor is added as a shell to enhance the gain from the quantum-dot core. This shell is designed to electronically isolate the core, funnel excitons to it, and reduce nonradiative Auger recombination. However, the s...