RW-spaces and compactness of function spaces for L-domains

AbstractThe purpose of this paper is to study the Lawson compactness of function spaces for L-domains. A basic notion of property RW for core compact spaces is introduced, which is proved to have a close relation to the Lawson compactness of function spaces for continuous L-domains as following: (1)Every Lawson compact continuous dcpo has property RW (via the Scott topology) and for each continuous L-domain, Lawson compactness is equivalent to property RW;(2)Let P be a continuous dcpo with a least element. Then [X→P] is compact continuous for every core compact space X with property RW iff P is compact continuous L-domain;(3)Let X be a core compact space. Then [X→P] is compact for every compact continuous L-domain P iff X has property RW

Free dcpo-algebras via directed spaces

Directed spaces are natural topological extensions of dcpos in domain theory and form a cartesian closed category. We will show that the D-completion of free algebras over a Scott space $\Sigma L$, on the context of directed spaces, are exactly the free dcpo-algebras over dcpo $L$, which reveals the close connection between directed powerspaces and powerdomains. By this result, we provide a topological representation of upper, lower and convex powerdomains of dcpos uniformly.Comment: 18 page

Resonant quantum coherence of magnetization at excited states in nanospin systems with different crystal symmetries

The quantum interference effects induced by the Wess-Zumino term, or Berry phase are studied theoretically in resonant quantum coherence of magnetization vector between degenerate excited states in nanometer-scale single-domain ferromagnets in the absence of an external magnetic field. By applying the periodic instanton method in the spin-coherent-state path integral, we evaluate the low-lying tunnel splittings between degenerate excited states of neighboring wells. And the low-lying energy level spectrum of m-th excited states are obtained with the help of the Bloch theorem in one-dimensional periodic potential.Comment: 23 pages, final version and accepted by Eur. Phys. J.

Non-equilibrium dynamics of simple spherical spin models

We investigate the non-equilibrium dynamics of spherical spin models with two-spin interactions. For the exactly solvable models of the d-dimensional spherical ferromagnet and the spherical Sherrington-Kirkpatrick model the asymptotic dynamics has for large times and for large waiting times the same formal structure. In the limit of large waiting times we find in both models an intermediate time scale, scaling as a power of the waiting time with an exponent smaller than one, and thus separating the time-translation invariant short-time dynamics from the aging regime. It is this time scale on which the fluctuation-dissipation regime is violated. Aging in these models is similar to that observed in spin glasses at the level of correlation functions, but different at the level of response functions, and thus different at the level of experimentally accessible quantities like the thermoremanent magnetization.Comment: 8 pages, 1 eps figur