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.