The random phase property and the Lyapunov Spectrum for disordered multi-channel systems

A random phase property establishing in the weak coupling limit a link between quasi-one-dimensional random Schrödinger operators and full random matrix theory is advocated. Briefly summarized it states that the random transfer matrices placed into a normal system of coordinates act on the isotropic frames and lead to a Markov process with a unique invariant measure which is of geometric nature. On the elliptic part of the transfer matrices, this measure is invariant under the unitaries in the hermitian symplectic group of the universality class under study. While the random phase property can up to now only be proved in special models or in a restricted sense, we provide strong numerical evidence that it holds in the Anderson model of localization. A main outcome of the random phase property is a perturbative calculation of the Lyapunov exponents which shows that the Lyapunov spectrum is equidistant and that the localization lengths for large systems in the unitary, orthogonal and symplectic ensemble differ by a factor 2 each. In an Anderson-Ando model on a tubular geometry with magnetic field and spin-orbit coupling, the normal system of coordinates is calculated and this is used to derive explicit energy dependent formulas for the Lyapunov spectrum

Disordered quantum wires: microscopic origins of the DMPK theory and Ohm's law

We study the electronic transport properties of the Anderson model on a strip, modeling a quasi one-dimensional disordered quantum wire. In the literature, the standard description of such wires is via random matrix theory (RMT). Our objective is to firmly relate this theory to a microscopic model. We correct and extend previous work (arXiv:0912.1574) on the same topic. In particular, we obtain through a physically motivated scaling limit an ensemble of random matrices that is close to, but not identical to the standard transfer matrix ensembles (sometimes called TOE, TUE), corresponding to the Dyson symmetry classes \beta=1,2. In the \beta=2 class, the resulting conductance is the same as the one from the ideal ensemble, i.e.\ from TUE. In the \beta=1 class, we find a deviation from TOE. It remains to be seen whether or not this deviation vanishes in a thick-wire limit, which is the experimentally relevant regime. For the ideal ensembles, we also prove Ohm's law for all symmetry classes, making mathematically precise a moment expansion by Mello and Stone. This proof bypasses the explicit but intricate solution methods that underlie most previous results.Comment: Corrects and extends arXiv:0912.157

Catalyseurs cuivre-zinc. X. Comparaison de quelques méthodes de préparation : coprécipitation, précipitations successives ou précurseur bimétallique

The comparison of different preparation procedures of Cu-ZnO catalysts has disclosed the formation of an unidentified copper-zinc phase in the case of precipitation methods. The size of the copper crystallites obtained after reduction is clearly related to the amount to this phase. Moreover, the catalytic activity in methanol synthesis from CO + CO2 + H2 mixture depends on the intermediate formation of this phase. The bimetallic precursor leads to catalyst that displays a lower activity correlated to sintering of copper during the reduction step

Hyperplastic cardiac sarcoma recurrence

Primary cardiac sarcomas are rare tumors with a median survival of 6-12 months. Data suggest that an aggressive multidisciplinary approach may improve patient outcome. We present the case of a male who underwent resection of cardiac sarcoma three times from the age of 32 to 34. This report discusses the malignant nature of cardiac sarcoma and the importance of postoperative multidisciplinary care