Diameter dependence of SiGe nanowire thermal conductivity

We theoretically compute the thermal conductivity of SiGe alloy nanowires as a function of nanowire diameter, alloy concentration, and temperature, obtaining a satisfactory quantitative agreement with experimental results. Our results account for the weaker diameter dependence of the thermal conductivity recently observed in Si$_{1-x}$Ge$_x$ nanowires ($x<0.1$), as compared to pure Si nanowires. We also present calculations in the full range of alloy concentrations, $0 \leq x \leq 1$, which may serve as a basis for comparison with future experiments on high alloy concentration nanowires.Comment: 3 fig

Second Order Freeness and Fluctuations of Random Matrices: I. Gaussian and Wishart matrices and Cyclic Fock spaces

We extend the relation between random matrices and free probability theory from the level of expectations to the level of fluctuations. We introduce the concept of "second order freeness" and derive the global fluctuations of Gaussian and Wishart random matrices by a general limit theorem for second order freeness. By introducing cyclic Fock space, we also give an operator algebraic model for the fluctuations of our random matrices in terms of the usual creation, annihilation, and preservation operators. We show that orthogonal families of Gaussian and Wishart random matrices are asymptotically free of second order.Comment: 46 pages, 13 figures, second revision adds explanations, figures, and reference

Real Second Order Freeness and Haar Orthogonal Matrices

We demonstrate the asymptotic real second order freeness of Haar distributed orthogonal matrices and an independent ensemble of random matrices. Our main result states that if we have two independent ensembles of random matrices with a real second order limit distribution and one of them is invariant under conjugation by an orthogonal matrix, then the two ensembles are asymptotically real second order free. This captures the known examples of asymptotic real second order freeness introduced by Redelmeier [R1, R2].Comment: 50 pages, revision has refreshed references and corrected typo