Approach to Equilibrium for a Class of Random Quantum Models of Infinite Range

We consider random generalizations of a quantum model of infinite range introduced by Emch and Radin. The generalizations allow a neat extension from the class l (1) of absolutely summable lattice potentials to the optimal class l (2) of square summable potentials first considered by Khanin and Sinai and generalised by van Enter and van Hemmen. The approach to equilibrium in the case of a Gaussian distribution is proved to be faster than for a Bernoulli distribution for both short-range and long-range lattice potentials. While exponential decay to equilibrium is excluded in the nonrandom l (1) case, it is proved to occur for both short and long range potentials for Gaussian distributions, and for potentials of class l (2) in the Bernoulli case. Open problems are discussed.

Structural Characterization of Rare-Earth Doped Yttrium Aluminoborate Laser Glasses Using Solid State NMR

The structure of laser glasses in the system (B(2)O(3))(0.6){(Al(2)O(3))(0.4-x)(Y(2)O(3))(x)} (0.1 <= x <= 0.25) has been investigated by means of (11)B, (27)Al, and (89)Y solid state NMR as well as Y-3d core-level X-ray photoelectron spectroscopy, (11)B magic-angle spinning (MAS) NMR spectra reveal that the majority of the boron atoms are three-coordinated, and a slight increase of four-coordinated boron content with increasing x can be noticed. (27)Al MAS NMR spectra show that the alumina species are present in the coordination states four, five and six. All of them are in intimate contact with both the three- and the four-coordinate boron species and vice versa, as indicated by (11)B/(27)Al rotational echo double resonance (REDOR) data. These results are consistent with the formation of a homogeneous, nonsegregated glass structure. For the first time, (89)Y solid state NMR has been used to probe the local environment of Y(3+) ions in a glass-forming system. The intrinsic sensitivity problem associated with (89)Y NMR has been overcome by combining the benefits of paramagnetic doping with those of signal accumulation via Carr-Purcell spin echo trains. Both the (89)Y chemical shifts and the Y-3d core level binding energies are found to be rather sensitive to the yttrium bonding state and reveal that the bonding properties of the yttrium atoms in these glasses are similar to those found in the model compounds YBO(3) and YAl(3)(BO(3))(4), Based on charge balance considerations as well as (11)B NMR line shape analyses, the dominant borate species are concluded to be meta- and pyroborate anions.