Glassy Random Matrix Models

This paper discusses Random Matrix Models which exhibit the unusual phenomena of having multiple solutions at the same point in phase space. These matrix models have gaps in their spectrum or density of eigenvalues. The free energy and certain correlation functions of these models show differences for the different solutions. Here I present evidence for the presence of multiple solutions both analytically and numerically. As an example I discuss the double well matrix model with potential $V(M)= -{\mu \over 2}M^2+{g \over 4}M^4$ where $M$ is a random $N\times N$ matrix (the $M^4$ matrix model) as well as the Gaussian Penner model with $V(M)={\mu\over 2}M^2-t \ln M$. First I study what these multiple solutions are in the large $N$ limit using the recurrence coefficient of the orthogonal polynomials. Second I discuss these solutions at the non-perturbative level to bring out some differences between the multiple solutions. I also present the two-point density-density correlation functions which further characterizes these models in a new university class. A motivation for this work is that variants of these models have been conjectured to be models of certain structural glasses in the high temperature phase.Comment: 25 pages, Latex, 7 Figures, to appear in PR

Gravitational Corrections for Supersymmetric Gauge Theories with Flavors via Matrix Models

We study the gravitational corrections to the F-term in four-dimensional N=1 U(N) gauge theories with flavors, using the Dijkgraaf-Vafa theory. We derive a compact formula for the annulus contribution in terms of the prime form on the matrix model curve. Remarkably, the full R^2 correction can be reproduced as a special momentum sector of a single c=1 CFT correlator, which closely resembles that in the bosonization of fermions on Riemann surfaces. The N=2 limit of the torus contribution agrees with the multi-instanton calculations as well as the topological A-model result. The planar contributions, on the other hand, have no counterpart in the topological gauge theories, and we speculate about the origin of these terms.Comment: 47 pages, 9 figures; Sign errors corrected. Figure 5 replaced. References adde

Epitaxial growth of heavily P-doped Si films at 450 °C by alternately supplied PH3 and SiH4

Epitaxial growth of heavily P-doped Si films at 450 °C by alternately supplied PH3 and SiH4 has been investigated using an ultraclean low-pressure chemical vapor deposition (CVD) system. By exposing the Si(100) surface to PH3 at a partial pressure of 0.26Pa at 450-750°C, two or three atomic-layers of P are adsorbed. Thermal desorption of P occurs at 650°C and only slightly at 450°C. By alternately supplied PH3 at 300-450°C and SiH4 at 450°C, epitaxial growth of heavily P-doped Si films of average P concentrations of ~1021cm-3 are achieved. In the case of 4 cycles of alternately supplied PH3 and SiH4 at 450°C, 26nm-thick P-doped epitaxial Si film, with the average P concentration of 6xl020cm-3 is formed. It is found that about 60 % of P is electrically active even in the heavily P-doped epitaxial Si film and the resistivity is as low as ∼30Ω.cm. By annealing the film at 550°C and above, it is found that the carrier concentration decreases and the resistivity increases. It is suggested that very low-resistive epitaxial Si film is formed by alternately supplied PH3 and SiH4 only at a very low-temperature such as 450°C

Calcination temperature dependent catalytic activity and stability of IrO2 – Ta2O5 anodes for oxygen evolution reaction in aqueous sulfate electrolytes

In this work, commercial IrO2-Ta2O5 anodes with a certain composition calcined at three different temperatures were investigated. The results show that the calcination temperature has a significant influence on the electrocatalytic activity for the oxygen evolution reaction (OER). This is attributed to the influence of the calcination temperature on the surface microstructure including the crystallinity and the preferred orientation of IrO2 crystallites of the IrO2-Ta2O5 binary oxide formed. The surface morphology of the anodes was revealed as mud-cracks surrounded by flat areas containing several scattered IrO2 nanocrystallites. The size of these nanocrystallites, which in turn contribute to the electrochemical active surface area, is dependent on calcination temperature. The (101)-surfaces of the IrO2 were found to have higher catalytic activity than (110) IrO2 with respect to the OER. The (101) IrO2 planes were dominating at low or moderate calcination temperatures, whereas the (110) IrO2 orientation was preferred at the highest calcination temperature. Accelerated lifetime tests of the investigated samples indicate that the (101) IrO2 is more stable (110) IrO2 during electrolysis. A moderate temperature is suggested as the best calcination temperature for this type of anode regarding the electrochemical active surface area, electrocatalytic activity and stability for OER in acidic aqueous electrolytes at operating conditions