Absence of symmetry breaking for systems of rotors with random interactions

We prove that Gibbs states for the Hamiltonian , with thes _x varying on theN-dimensional unit sphere, obtained with nonrandom boundary conditions (in a suitable sense), are almost surely rotationally invariant if withJ _xy i.i.d. bounded random variables with zero average, 1 in one dimension, and 2 in two dimensions.     

Dynamics of the current-driven Josephson junction

The irreversible macroscopic dynamics of the Josephson junction coupled to external wires acting as a current source is derived rigorously from the underlying microscopic Hamiltonian quantum mechanics. The external systems are treated in the singular coupling limit. The use of this limit is explicitly justified via an interpretation of the singular coupling limit in terms of the relative magnitudes of system, reservoir, and coupling energies. The qualitative behavior of the macroscopic dynamical equations is shown to depend sensitively and crucially on the interaction between the wires and the superconductors and on the size of the wires: the dc Josephson effect only happens when one lets Cooper pairs be driven into the junction by collective (i.e., small) reservoirs.     

Synthesis on the basis of electrogenerated carbenes

A series ofS _N2 reactions with halomethanes as substrates and the corresponding anions as nucleophiles were studied by the semiempirical MNDO and AM1 methods, taking into account solvent effects. Analysis of the kinetics, structures of reagents, intermediates and products, and charge distribution in them allows one to draw the conclusion that the retardation ofS _N2 reactions is stronger in solvents than in the gas phase, and the rates of reactions involving anions with a lower number of halogen atoms are higher.For Part 8 see Ref. 1.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 11, pp. 2148–2154, November, 1995.This work was partially financially supported by the International Science Foundation (Grant No. MHYOO).     

Synthesis, Structure and Optical Properties of Cerium(Ⅲ) Triphosphate CeP3O9

The single crystal and crystallized powder of triphosphate CeP3O9 have been synthesized, and the space group of CeP3O9 has been determined to be C2221 with the cell parameters ofa = 8.6059, b = 11.2437, c = 7.3518 (A), V= 711.4(3) (A)3, Z= 4, Dc = 3.520 g/cm3, F(000) = 700,R = 0.0377 and wR = 0.0930. The absorption and emission spectra have been measured, for which the strongest absorption and emission peaks are located at 280 and 320 nm, respectively. The density of state (DOS) and dielectric function have been calculated by the DFT method. The crystal is transparent provided the wavelength is larger than 341 nm, and the observed ultraviolet cut-off edge is at about 350 nm for a polycrystalline power sample. It is possible that the triphosphate CeP3O9 will become an ultraviolet emission material.     

DFT Calculations of the Ionization Potential and Electron Affinity of Alaninamide

Adiabatic and vertical ionization potentials (IPs) and valence electron affinities (EAs) of alaninamide in gas phase have been determined using density functional theory (BLYP,B3LYP,B3P86) methods with 6-311++G(d,p) basis set,respectively. IPs and EAs of alaninamide in solutions have been calculated at the B3LYP/6-311++G(d,p) level. Five possible conformers of alaninamide and their charged states have been optimized employing density functional theory B3LYP method with 6-311++(d,p) basis set,respectively.     

Lifschitz singularities for periodic operators plus random potentials

UsingX-bounding (lower bounds by Laplacians with mixed boundary conditions and discrete analogs), we obtain the Lifschitz exponent at the bottom of the spectrum for random operators of typeH =T+V , withT a (periodic) generator of a positivity-preserving semigroup, extending results by Kirsch and Simon.