Quantum phase transition in the Plaquette lattice with anisotropic spin exchange

I study the influence of anisotropic spin exchange on a quantum phase transition in the Plaquette lattice driven by the purely quantum effect of singlet formation. I study the influence of i) a Dzyaloshinskii-Moriya exchange and ii) four spin exchange on the transition point by evaluating spin--spin correlations and the spin gap with exact diagonalization. The results point to a stabilization of the Neel-like long range order when the Dzyaloshinskii-Moriya exchange is added, whereas the four-spin exchange might stabilize the singlet order as well as the Neel-like order depending on its strength.Comment: LaTeX article with 4 pages and 3 figures, prepared with material for the ICM 200

On Generalizing Decidable Standard Prefix Classes of First-Order Logic

Recently, the separated fragment (SF) of first-order logic has been introduced. Its defining principle is that universally and existentially quantified variables may not occur together in atoms. SF properly generalizes both the Bernays-Sch\"onfinkel-Ramsey (BSR) fragment and the relational monadic fragment. In this paper the restrictions on variable occurrences in SF sentences are relaxed such that universally and existentially quantified variables may occur together in the same atom under certain conditions. Still, satisfiability can be decided. This result is established in two ways: firstly, by an effective equivalence-preserving translation into the BSR fragment, and, secondly, by a model-theoretic argument. Slight modifications to the described concepts facilitate the definition of other decidable classes of first-order sentences. The paper presents a second fragment which is novel, has a decidable satisfiability problem, and properly contains the Ackermann fragment and---once more---the relational monadic fragment. The definition is again characterized by restrictions on the occurrences of variables in atoms. More precisely, after certain transformations, Skolemization yields only unary functions and constants, and every atom contains at most one universally quantified variable. An effective satisfiability-preserving translation into the monadic fragment is devised and employed to prove decidability of the associated satisfiability problem.Comment: 34 page

Self-organizing, Collision-free, Multi-channel Convergecast

Intenerg

Chern character for totally disconnected groups

In this paper we construct a bivariant Chern character for the equivariant $KK$-theory of a totally disconnected group with values in bivariant equivariant cohomology in the sense of Baum and Schneider. We prove in particular that the complexified left hand side of the Baum-Connes conjecture for a totally disconnected group is isomorphic to cosheaf homology. Moreover, it is shown that our transformation extends the Chern character defined by Baum and Schneider for profinite groups

Equivariant local cyclic homology and the equivariant Chern-Connes character

We define and study equivariant analytic and local cyclic homology for smooth actions of totally disconnected groups on bornological algebras. Our approach contains equivariant entire cyclic cohomology in the sense of Klimek, Kondracki and Lesniewski as a special case and provides an equivariant extension of the local cyclic theory developped by Puschnigg. As a main result we construct a multiplicative Chern-Connes character for equivariant KK-theory with values in equivariant local cyclic homology.Comment: 38 page

Interactive comment on "Latitudinal differences in the amplitude of the OAE-2 carbon isotopic excursion: pCO2 and paleoproductivity" by E. C. van Bentum et al.

Interactive comment on Biogeosciences Discuss., 8, 6191, 2011