Localization in the ground state of a disordered array of quantum rotators

We consider the zero-temperature behavior of a disordered array of quantum rotators given by the finite-volume Hamiltonian: $$H_\Lambda = - \mathop \Sigma \limits_{x \in \Lambda } \frac{{h(x)}}{2}\frac{{\partial ^2 }}{{\partial \varphi (x)^2 }} - J\mathop \Sigma \limits_{\left\langle {x,y} \right\rangle \in \Lambda } \cos (\varphi (x) - \varphi (y))$$ , wherex,y∈Z ^d , 〈,〉 denotes nearest neighbors inZ ^d ;J>0 andh={h(x)>0,x∈Z ^d } are independent identically distributed random variables with common distributiondμ(h), satisfying ∫h ^?δ dμ(h)<∞ for some δ>0. We prove that for anym>0 it is possible to chooseJ(m) sufficiently small such that, if 0<J<J(m), for almost every choice ofh and everyx∈Z ^d the ground state correlation function satisfies $$\left\langle {\cos (\varphi (x) - \varphi (y))} \right\rangle \leqq C_{x,h,J} e^{ - m\left| {x - y} \right|} $$ for ally∈Z ^d withC _x,h,J <∞.     

Analyticity of the density of states in the anderson model on the Bethe lattice

Let H=1/2+V on l²(B), whereB is the Bethe lattice andV(x),x B, are i.i.d.r.v.'s with common probability distribution. It is shown that for distributions sufficiently close to the Cauchy distribution, the density of states(E) is analytic in a strip about the real axis.     

Spectroscopic investigation and thermal behavior of new carbonyl complexes [M(CO)4(N—N)(CuX)], (M = W,Mo; N—N = 2,2′-bipyridine, 1,10-phenanthroline; X = Cl,SCN)

[M(CO)₄(N—N)] reacts with CuCl to give new heterobimetallic metal carbonyls of the type [M(CO)₄(N—N)(CuCl)], M = W, Mo; N—N = 2,2-bipyridine (bipy), 1,10-phenanthroline (phen). Reactions of [M(CO)₄(N—N)(CuCl)] with NaSCN produced the series of complexes of general formula [M(CO)₄(N—N)(CuSCN)]. The i.r. spectral of all the bimetallic carbonyls exhibited the general four (CO) band patterns of the precursors. The u.v.–vis. spectral data for precursors and products showed bands associated with * (nitrogen ligands), dd (intrametal), as well as MLCT d* (nitrogen ligands) and MLCT d *(CO) transitions. The [M(CO)₄(N—N)(CuX)] (X = Cl, SCN) emission spectra showed only one band associated with the MLCT transition. The t.g. curves revealed a stepwise loss of CO groups. The initial decomposition temperatures of the [M(CO)₄(N—N)(CuX)] series suggest that the bimetallic compounds are indeed thermally less stable than their precursors, and the X-ray data showed the formation of MO₃, CuMO₄, Cu₂O and CuO as final decomposition products, M = W, Mo. The spectroscopic data suggests that the heterobimetallic compounds are polymeric.     

Symmetric-group algebraic variational solutions for Heisenberg models at finite temperature

The Heisenberg spin Hamiltonian for a collection of N spin-1/2 sites is viewed, as favored by Professor Matsen, to be an element of the group algebra of the symmetric group ??_N. Several computationally tractable, variational group–algebraic approximations for the finite-temperature density matrix are made so as to minimize the Gibb's free–energy functional. Relations to previous quite differently motivated approximations are identified, though improvements are noted with the present approach.     

Solid State NMR and TG/MS Study on the Transformation of Methyl Groups During Pyrolysis of Preceramic Precursors to SiOC Glasses

The sol-gel method was used to prepare two different starting gels containing SiCH₃-groups for the preparation of SiOC ceramics. To understand the role of Si—H bonds in the incorporation of carbon into the SiOC network, gels prepared from a 1:2 mixture of triethoxysilane and methyldiethoxysilane (T^HD^H2) and solely methyltriethoxysilane (T^Me) were investigated. Thermogravimetric analysis coupled with mass spectroscopy (TG-MS) in inert atmosphere was performed to attain an insight into the decomposition reactions involved during gel-glass transformation. Samples calcined at different temperatures up to 1000°C were characterized by ²⁹Si and ¹³C magic angle spinning nuclear magnetic resonance (MAS-NMR) spectroscopy. The presence of SiH groups in the starting gel allows an efficient conversion of Si—CH₃ groups into CSi₄ sites at lower temperatures. As a result, despite a much lower amount of carbon in the starting T^HD^H2 gel (C/Si = 0.33) compared to the T^Me gel (C/Si = 1), the amount of carbon inserted into the SiOC network of both glasses is equivalent, but the T^Me sample contains the 10 fold amount of free carbon.     

Octasubstituted metal-free phthalocyanine as core of phosphorus dendrimers: a probe for the properties of the internal structure

The synthesis of a new family of phosphorus dendrimers built from an octasubstituted metal-free phthalocyanine core is described up to generation 5. This core is used as a sensor and a probe for analyzing the properties of the internal structure and the influence of each structural part (core, branches, surface) upon the whole structure. UV-visible spectra show both a hyperchromic and bathochromic effect on the Q-bands with increasing generation, indicating that the chromophore is more isolated, and that the dendritic shell mimics a highly polar solvent. There is no evidence for aggregation, except for generation 0, showing again the isolation of the core. However, the dendritic shell is permeable to aqueous acids and bases, as demonstrated by the reversible splitting of the Q-band in an acidic medium (neutral form of the phthalocyanine) and the single Q-band in a basic medium (dianionic form), even for generation 4. The fluorescence quantum yield for the neutral form increases with increasing generation. The dianionic form of generation 0 is poorly fluorescent, whereas generations 3 and 4 (G3 and G4) exhibit better fluorescence. The cores of G3 and G4 are highly sensitive optical sensors for H3O+ and OH-. These experiments are carried out in THF/water mixtures, and the influence of water on the structure has been checked. The hydrodynamic radius of generation 4 is measured by NMR diffusion (pulse gradient spin-echo) experiments. R(H) varies from 35.4 A at 4 mol % of water to 32.5 A at 64 mol % of water in THF, indicating the hydrophobic nature of these dendrimers.     

Improving splitless injection with electronic pressure programming

An experimental injection port has been designed for split or splitless sample introduction in capillary gas chromatography; the inlet uses electronic pressure control, in order that the column head pressure may be set from the GC keyboard, and the inlet may be used in the constant flow or constant pressure modes. Alternatively, the column head pressure may be programmed up or down during a GC run in a manner analogous to even temperature programming. Using electronic pressure control, a method was developed which used high column head pressures (high column flow rates) at the time of injection, followed by rapid reduction of the pressure to that required for optimum GC separation. In this way, high flow rates could be used at the time of splitless injection to reduce sample discrimination, while lower flow rates could be used for the separation. Using this method, up to 5 μl of a test sample could be injected in the splitless mode with no discrimination; in another experiment, 2.3 times as much sample was introduced into the column by using electronic pressure programming. Some GC peak broadening was observed in the first experiment.