In the paper we study the endomorphim semigroup of a general quantum polynomial ring, its finite groups of automorphisms and homological properties of this ring as a module over the skew group ring of a finite group of automorphisms. Moreover properties of the division ring of fractions are considered.

The main goal of this paper is to give a unified description for the structure of the small quantum cohomology rings for all homogeneous spaces of SL n (C). The quantum cohomology ring of a smooth projective variety, or, more generally of a symplectic manifold, has been introduced by physicists in the study of topo-logical field theories ([V], [W]). In the past few years, the highly non-trivial...

Bloch-like oscillations induced by charge discreteness in quantum mesoscopic rings. We study the effect of charge discreteness in a quantum mesoscopic ring wih inductance L. The ring is pierced by a time depending external magnetic field. When the external magnetic flux varies uniformly, the current induced in the ring oscillates with a frequency proportional to the charge discreteness and the ...

Within local-spin-density functional theory, we have investigated the “dissociation” of few-electron circular vertical semiconductor double quantum ring artificial molecules at zero magnetic field as a function of interring distance. In a first step, the molecules are constituted by two identical quantum rings. When the rings are quantum mechanically strongly coupled, the electronic states are ...

We want to define a deformation of the flag variety F (r1, . . . , rm, n) of SLn(k) the special linear group of k , where k is an algebraically closed field of characteristic 0. We will construct the quantum flag ring as a subalgebra of kq[SLn(k)], the quantum SLn(k) and we then will exhibit it in terms of generators and relations in the case in which kq is replaced by a suitable local ring in ...

Let V be a vector space with a nondegenerate symmetric form and OG be the orthogonal Grassmannian which parametrizes maximal isotropic subspaces in V . We give a presentation for the (small) quantum cohomology ring QH∗(OG) and show that its product structure is determined by the ring of P̃ -polynomials. A ‘quantum Schubert calculus’ is formulated, which includes quantum Pieri and Giambelli formu...

The ring-opening reaction of a trifluorinated indolylfulgide has been studied as a function of temperature and optical pre-excitation where it was found that reaction times decreased as temperature increased from 10.3 ps at 12 degrees C to 7.6 ps at 60 degrees C. Simultaneously, the quantum yields for the ring-opening reaction grew from 3.1% (12 degrees C) to 5.0% (60 degrees C). When the react...

The space of m-harmonic polynomials related to a Coxeter group G and a multiplicity function m on its root system is defined as the joint kernel of the properly gauged invariant integrals of the corresponding generalised quantum Calogero-Moser problem. The relation between this space and the ring of all quantum integrals of this system (which is isomorphic to the ring of corresponding quasiinva...

We study the complexity of some computational problems on finite black-box rings whose elements are encoded as strings of a given length and the ring operations are performed by a black-box oracle. We give a polynomial-time quantum algorithm to compute a basis representation for a given black-box ring. Using this result we obtain polynomial-time quantum algorithms for several natural computatio...

The quantum critical coupling conditions, where single-photon transmission goes to zero, for systems of a coupled ring resonator and atom in a one-dimensional single-mode waveguide are discussed. The quantum critical coupling conditions could be achieved even with nonvanishing intrinsic losses of the resonator and the atom, with intermode backscattering between the whispering-gallery modes of t...