Clearing algorithms and network centrality

I show that the solution of a standard clearing model commonly used in contagion analyses for financial systems can be expressed as a specific form of a generalized Katz centrality measure under conditions that correspond to a system-wide shock. This result provides a formal explanation for earlier empirical results which showed that Katz-type centrality measures are closely related to contagiousness. It also allows assessing the assumptions that one is making when using such centrality measures as systemic risk indicators. I conclude that these assumptions should be considered too strong and that, from a theoretical perspective, clearing models should be given preference over centrality measures in systemic risk analyses

Dynamical phase transition for a quantum particle source

We analyze the time evolution describing a quantum source for noninteracting particles, either bosons or fermions. The growth behaviour of the particle number (trace of the density matrix) is investigated, leading to spectral criteria for sublinear or linear growth in the fermionic case, but also establishing the possibility of exponential growth for bosons. We further study the local convergence of the density matrix in the long time limit and prove the semiclassical limit.Comment: 24 pages; In the new version, we added several references concerning open quantum systems and present an extended result on linear particle production in the fermionic cas

A Kohn-Sham system at zero temperature

An one-dimensional Kohn-Sham system for spin particles is considered which effectively describes semiconductor {nano}structures and which is investigated at zero temperature. We prove the existence of solutions and derive a priori estimates. For this purpose we find estimates for eigenvalues of the Schr\"odinger operator with effective Kohn-Sham potential and obtain $W^{1,2}$-bounds of the associated particle density operator. Afterwards, compactness and continuity results allow to apply Schauder's fixed point theorem. In case of vanishing exchange-correlation potential uniqueness is shown by monotonicity arguments. Finally, we investigate the behavior of the system if the temperature approaches zero.Comment: 27 page

Wigner Measure Propagation and Conical Singularity for General Initial Data

We study the evolution of Wigner measures of a family of solutions of a Schr\"odinger equation with a scalar potential displaying a conical singularity. Under a genericity assumption, classical trajectories exist and are unique, thus the question of the propagation of Wigner measures along these trajectories becomes relevant. We prove the propagation for general initial data.Comment: 24 pages, 1 figur

A Study of the Residual 39Ar Content in Argon from Underground Sources

The discovery of argon from underground sources with significantly less 39Ar than atmospheric argon was an important step in the development of direct-detection dark matter experiments using argon as the active target. We report on the design and operation of a low background detector with a single phase liquid argon target that was built to study the 39Ar content of the underground argon. Underground argon from the Kinder Morgan CO2 plant in Cortez, Colorado was determined to have less than 0.65% of the 39Ar activity in atmospheric argon.Comment: 21 pages, 10 figure