On the 1/n expansion

The 1/n expansion is considered for then-component non-linear -model (classical Heisenberg model) on a lattice of arbitrary dimensions. We show that the expansion for correlation functions and free energy is asymptotic, for all temperatures above the spherical model critical temperature. Furthermore, the existence of a mass gap is established for these temperatures andn sufficiently large.Supported in part by the National Science Foundation under Grant PHY 79-16812     

Expanding the hydride chemistry: antiperovskites A3MO4H (A = Rb,Cs; M = Mo,W) introducing the transition oxometalate hydrides

The four compounds A₃MO₄H (A = Rb, Cs; M = Mo, W) are introduced as the first members of the new material class of the transition oxometalate hydrides. The compounds are accessible via a thermal synthesis route with carefully controlled conditions. Their crystal structures were solved by neutron diffraction of the deuterated analogues. Rb₃MoO₄D, Cs₃MoO₄D and Cs₃WO₄D crystallize in the antiperovskite-like K₃SO₄F-structure type, while Rb₃WO₄D adopts a different orthorhombic structure. ²H MAS NMR, Raman spectroscopy and elemental analysis prove the abundance of hydride ions next to oxometalate ions and experimental findings are supported by quantum chemical calculations. The tetragonal phases are direct and wide band gap semiconductors arising from hydride states, whereas Rb₃WO₄H shows a unique, peculiar valence band structure dominated by hydride states.

The synthesis, structures and electronic properties of the first four heteroanionic compounds containing both hydride and transition oxometalate ions are reported.     

Structural and magnetic properties of pulsed laser deposited SrRuO3/CoFe2O4/La2/3Sr1/3MnO3 magnetic oxide heterostructures on SrTiO3(001) and MgO(001)

We report on the growth of all-oxide SrRuO₃/CoFe₂O₄/La_2/3Sr_1/3MnO₃ and La_2/3Sr_1/3MnO₃/CoFe₂O₄/SrRuO₃ heterostuctures on SrTiO₃(001) and MgO(001) substrates by pulsed laser deposition. Structural analyses by X-ray diffraction and transmission electron microscopy clearly indicate the preservation of epitaxial relations when the La_2/3Sr_1/3MnO₃ layer is grown first, whereas trilayers with SrRuO₃ at the bottom are more disordered. Both the substrate material and the deposition sequence strongly influence the formation of various structural defects such as interfacial dislocations and sub-grain structures, and this is clearly reflected by a reduction of the saturation magnetization in the top electrode. When the substrate material and the deposition sequence are correctly chosen, however, the magnetic moments of the La_2/3Sr_1/3MnO₃ and SrRuO₃ layers reverse independently, and the La_2/3Sr_1/3MnO₃ layer retains bulk-like magnetic properties.     

A Comprehensive Study on the Full Series of Alkali-Metal Selenocyanates AI[SeCN] (AI=Li−Cs)

The full series of quasibinary alkali-metal selenocyanates was synthesized either by oxidation of the respective cyanides (A=Li−Rb) or by metathesis (A=Cs). For Li[SeCN] only ball-milling and subsequent annealing led to the isolation of the quasibinary selenocyanate. Their structures were refined from single-crystal and powder X-ray data. The respective solid-state IR and Raman spectra were interpreted with the aid of solid-state quantum-mechanical calculations and DSC-TGA measurements allowed for extraction of melting points. Only for Li[SeCN] a possible phase transition was observed that is discussed on the basis of VT-PXRD experiments. It is also the only quasibinary selenocyanate to form a hydrate (Li[SeCN] ⋅ 2H₂O).     

Mukaiyama–Michael Reactions with trans‐2,5‐Diarylpyrrolidine Catalysts: Enantioselectivity Arises from Attractive Noncovalent Interactions,Not from Steric Hindrance

The scope of the enantioselective Mukaiyama–Michael reactions catalyzed by trans‐2,5‐diphenylpyrrolidine has been expanded to include both α‐ and β‐substituted enals. However, the rationalization of the observed enantioselectivity is far from obvious since the catalyst is not very sterically hindered. DFT calculations were carried out to rationalize the observed stereoselectivities. Transition states of the C?C bond formation between iminium intermediates and silyloxyfurans were located and their relative energies were used to estimate the stereoselectivity data. We find excellent agreement between the predicted and observed stereoselectivities. The analysis of intermolecular forces reveals that the enantioselectivity is mostly due to stabilizing noncovalent interactions between the reacting partners, not due to steric hindrance. The role of attractive noncovalent interactions in enantioselective catalysis may be underappreciated.     

Quantum Diffusion and Eigenfunction Delocalization in a Random Band Matrix Model

We consider Hermitian and symmetric random band matrices H in d ≥ 1 dimensions. The matrix elements H _xy , indexed by \({x,y \in \Lambda \subset \mathbb{Z}^d}\), are independent, uniformly distributed random variables if \({\lvert{x-y}\rvert}\) is less than the band width W, and zero otherwise. We prove that the time evolution of a quantum particle subject to the Hamiltonian H is diffusive on time scales \({t\ll W^{d/3}}\). We also show that the localization length of the eigenvectors of H is larger than a factor W ^d/6 times the band width. All results are uniform in the size \({\lvert{\Lambda}\rvert}\) of the matrix.     

Packing dimension and Ahlfors regularity of porous sets in metric spaces

Let X be a metric measure space with an s-regular measure μ. We prove that if A ì X{A\subset X} is r{\varrho} -porous, then dim_p(A) ￡ s-cr^s{{\rm {dim}_p}(A)\le s-c\varrho^s} where dim_p is the packing dimension and c is a positive constant which depends on s and the structure constants of μ. This is an analogue of a well known asymptotically sharp result in Euclidean spaces. We illustrate by an example that the corresponding result is not valid if μ is a doubling measure. However, in the doubling case we find a fixed N ì X{N\subset X} with μ(N) = 0 such that dim_p(A) ￡ dim_p(X)-c(log\tfrac1r)^-1r^t{{\rm {dim}_p}(A)\le{\rm {dim}_p}(X)-c(\log \tfrac1\varrho)^{-1}\varrho^t} for all r{\varrho} -porous sets A ì X\ N{A \subset X{\setminus} N} . Here c and t are constants which depend on the structure constant of μ. Finally, we characterize uniformly porous sets in complete s-regular metric spaces in terms of regular sets by verifying that A is uniformly porous if and only if there is t < s and a t-regular set F such that A ì F{A\subset F} .     

SU(2) Chern-Simons theory at genus zero

We present a detailed study of the Schrödinger picture space of states in theSU(2) Chern-Simons topological gauge theory in the simplest geometry. The space coincides with that of the solutions of the chiral Ward identities for the WZW model. We prove that its dimension is given by E. Verlinde's formulae.