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.

All solid-state electrochromic devices with gelatin-based electrolyte

6 x 8cm(2) electrochromic devices (ECDs) with the configuration K-glass/EC-layer/electrotype/ion-storage (IS) layer/K-glass, have been assembled using Nb2O5:Mo EC layers, a (CeO2)(0.81)-TiO2 IS-layer and a new gelatin electrolyte containing Li+ ions. The structure of the electrolyte is X-ray amorphous. Its ionic conductivity passed by a maximum of 1.5 x 10(-5) S/CM for a lithium concentration of 0.3g/15ml. The value increases with temperature and follows an Arrhenius law with an activation energy of 49.5 kJ/mol. All solid-state devices show a reversible gray coloration, a long-term stability of more than 25,000 switching cycles (+/- 2.0 V/90 s), a transmission change at 550 nm between 60% (bleached state) and 40% (colored state) corresponding to a change of the optical density (Delta OD = 0. 15) with a coloration efficiency increasing from 10cm(2)/C (initial cycle) to 23cm(2)/C (25,000th cycle). (c) 2007 Elsevier B.V. All rights reserved.