On the environmental decoherence and spin interference in mesoscopic loop structures

Mechanisms of ‘environmental decoherence’ such as surface scattering, Elliot–Yafet process and precession mechanisms, as well as their influence on the spin phase relaxation are considered and compared. It is shown that the ‘spin ballistic’ regime is possible, when the phase relaxation length for the spin part of the wave function (L^(s)) is much greater than the phase relaxation length for the ‘orbital part’ (L^(e)). In the presence of an additional magnetic field, the spin part of the electron's wave function (WF) acquires a phase shift due to additional spin precession about that field. If the structure length L is chosen to be L^(s)>L>L^(e), it is possible to ‘wash out’ the quantum interference related to the phase coherence of the ‘orbital part’ of the WF, retaining at the same time that related to the phase coherence of the spin part and, hence, to reveal corresponding conductance oscillations.     

On nondegenerate coupling forms

The aim of the present paper is to investigate new classes of symplectically fat fibre bundles. We prove a general existence theorem for fat vectors with respect to the canonical invariant connections. Based on this result we give new proofs of some constructions of symplectic structures. This includes twistor bundles and locally homogeneous complex manifolds. The proofs are conceptually simpler and allow for obtaining more general results.     

On fundamental groups of symplectically aspherical manifolds

A smooth manifold M is called symplectically aspherical if it admits a symplectic form with |₂(M) = 0. It is easy to see that, unlike in the case of closed symplectic manifolds, not every finitely presented group can be realized as the fundamental group of a closed symplectically aspherical manifold. The goal of the paper is to study the fundamental groups of closed symplectically aspherical manifolds. Motivated by some results of Gompf, we introduce two classes of fundamental groups ₁(M) of symplectically aspherical manifolds M. The first one consists of fundamental groups of such M with ₂(M)=0, while the second with ₂(M)0. Relations between these classes are discussed. We show that several important (classes of) groups can be realized in both classes, while some groups can be realized in the first class but not in the second one. Also, we notice that there are some interesting dimensional phenomena in the realization problem. The above results are framed by a general study of symplectically aspherical manifolds. For example, we find some conditions which imply that the Gompf sum of symplectically aspherical manifolds is symplectically aspherical, or that a total space of a bundle is symplectically aspherical.Mathematics Subject Classification (1991): 57R15, 53D05, 14F35     

Cyclic homology of certain topological spaces formal in the sense of Sullivan

Translated from Matematicheskie Zametki, Vol. 50, No. 6, pp. 131–141, December, 1991.     

Reconstruction of quantum well potentials

The intertwining operator technique is applied to the generalized Schrödinger equation with a position-dependent effective mass. It is shown on concrete examples how to construct the quantum well potential with a desired spectrum for the Schrödinger equation with a nonhermitian kinetic energy operator.     

Answer set programming in intuitionistic logic

As a demonstration of the flexibility of constructive mathematics, we propose an interpretation of propositional answer set programming (ASP) in terms of intuitionistic proof theory, in particular in terms of simply typed lambda calculus. While connections between ASP and intuitionistic logic are well-known, they usually take the form of characterizations of stable models with the help of some intuitionistic theories represented by specific classes of Kripke models. As such the known results are model-theoretic rather than proof-theoretic. In contrast, we offer an explanation of ASP using constructive proofs.     

Exotic smooth structures and symplectic forms on closed manifolds

In this paper we discuss relations between symplectic forms and smooth structures on closed manifolds. Our main motivation is the problem if there exist symplectic structures on exotic tori. This is a symplectic generalization of a problem posed by Benson and Gordon. We give a short proof of the (known) positive answer to the original question of Benson and Gordon that there are no Kähler structures on exotic tori. We survey also other related results which give an evidence for the conjecture that there are no symplectic structures on exotic tori.