A Remark on the Deformation of GNS Representations of *-Algebras

Motivated by deformation quantization we investigate the algebraic GNS construction of *-representations of deformed *-algebras over ordered rings and compute their classical limit. The question if a GNS representation can be deformed leads to the deformation of positive linear functionals. Various physical examples from deformation quantization like the Bargmann-Fock and the Schr{\"o}dinger representation as well as KMS functionals are discussed.Comment: LaTeX2e, 8 page

Magnetic Cluster Excitations

Magnetic clusters, i.e., assemblies of a finite number (between two or three and several hundred) of interacting spin centers which are magnetically decoupled from their environment, can be found in many materials ranging from inorganic compounds, magnetic molecules, artificial metal structures formed on surfaces to metalloproteins. The magnetic excitation spectra in them are determined by the nature of the spin centers, the nature of the magnetic interactions, and the particular arrangement of the mutual interaction paths between the spin centers. Small clusters of up to four magnetic ions are ideal model systems to examine the fundamental magnetic interactions which are usually dominated by Heisenberg exchange, but often complemented by anisotropic and/or higher-order interactions. In large magnetic clusters which may potentially deal with a dozen or more spin centers, the possibility of novel many-body quantum states and quantum phenomena are in focus. In this review the necessary theoretical concepts and experimental techniques to study the magnetic cluster excitations and the resulting characteristic magnetic properties are introduced, followed by examples of small clusters demonstrating the enormous amount of detailed physical information which can be retrieved. The current understanding of the excitations and their physical interpretation in the molecular nanomagnets which represent large magnetic clusters is then presented, with an own section devoted to the subclass of the single-molecule magnets which are distinguished by displaying quantum tunneling of the magnetization. Finally, some quantum many-body states are summarized which evolve in magnetic insulators characterized by built-in or field-induced magnetic clusters. The review concludes addressing future perspectives in the field of magnetic cluster excitations.Comment: 59 pages, 64 figures, to appear in Rev. Mod. Phy

High-Frequency Electron-Spin-Resonance Study of the Octanuclear Ferric Wheel CsFe8_8

High-frequency ($f$ = 190 GHz) electron paramagnetic resonance (EPR) at magnetic fields up to 12 T as well as Q-band ($f$ = 34.1 GHz) EPR were performed on single crystals of the molecular wheel CsFe$_8$. In this molecule, eight Fe(III) ions, which are coupled by nearest-neighbor antiferromagnetic (AF) Heisenberg exchange interactions, form a nearly perfect ring. The angle-dependent EPR data allow for the accurate determination of the spin Hamiltonian parameters of the lowest spin multiplets with $S \leq$ 4. Furthermore, the data can well be reproduced by a dimer model with a uniaxial anisotropy term, with only two free parameters $J$ and $D$. A fit to the dimer model yields $J$ = -15(2) cm$^{-1}$ and $D$ = -0.3940(8) cm$^{-1}$. A rhombic anisotropy term is found to be negligibly small, $E$ = 0.000(2) cm$^{-1}$. The results are in excellent agreement with previous inelastic neutron scattering (INS) and high-field torque measurements. They confirm that the CsFe$_8$ molecule is an excellent experimental model of an AF Heisenberg ring. These findings are also important within the scope of further investigations on this molecule such as the exploration of recently observed magnetoelastic instabilities.Comment: 21 pages, 8 figures, accepted for publication in Inorganic Chemistr

Hierarchic Superposition Revisited

Many applications of automated deduction require reasoning in first-order logic modulo background theories, in particular some form of integer arithmetic. A major unsolved research challenge is to design theorem provers that are "reasonably complete" even in the presence of free function symbols ranging into a background theory sort. The hierarchic superposition calculus of Bachmair, Ganzinger, and Waldmann already supports such symbols, but, as we demonstrate, not optimally. This paper aims to rectify the situation by introducing a novel form of clause abstraction, a core component in the hierarchic superposition calculus for transforming clauses into a form needed for internal operation. We argue for the benefits of the resulting calculus and provide two new completeness results: one for the fragment where all background-sorted terms are ground and another one for a special case of linear (integer or rational) arithmetic as a background theory