arXiv subjects
Publications and source records attributed to M. Plum.
The present white paper is submitted as part of the "Snowmass" process to help inform the long-term plans of the United States Department of Energy and the National Science Foundation for high-energy physics. It summarizes the science questions driving the Ultra-High-Energy Cosmic-Ray (UHECR) community and provides recommendations on the strategy to answer them in the next two decades.
This paper considers the propagation of TE-modes in photonic crystal waveguides. The waveguide is created by introducing a linear defect into a periodic background medium. Both the periodic background problem and the perturbed problem are modelled by a divergence type equation. A feature of our analysis is that we allow discontinuities in the coefficients of the operator, which is required to model many photonic crystals. Using the Floquet-Bloch theory in negative order Sobolev spaces, we characterize the precise number of eigenvalues created by the line defect in terms of the band functions of the original periodic background medium for arbitrarily weak defects.
The spectrum of periodic differential operators typically exhibits a band-gap structure. In this paper, we will consider perturbations to periodic differential operators and investigate the spectrum the perturbation induces in the gaps. More specifically, we consider the operator $$ L_0 =-\frac{1}{\eps_0(x,y,z)}Δ$$ in $\R^3$ with $\eps_0$ periodic in all three directions. The perturbation is introduced by replacing $\eps_0$ by $\eps_0+\eps_1$ where we assume that $\eps_1$ is still periodic in one direction, but compactly supported in the remaining two directions, creating a line defect. We will show that even small perturbations $\eps_1$ lead to additional spectrum in the spectral gaps of the unperturbed operator $L_0$ and investigate some properties of the spectrum that is created.
VISPA is a novel development environment for high energy physics analyses, based on a combination of graphical and textual steering. The primary aim of VISPA is to support physicists in prototyping, performing, and verifying a data analysis of any complexity. We present example screenshots, and describe the underlying software concepts.
The Weyl-Sims classification for a second-order ordinary differential equation with general complex coefficients is investigated. Connections are then established between the associated m-function and the spectral properties of maximal-accretive realisations of the differential expression.
The paper reports on computation of verified enclosures for the Titchmarsh-Weyl m-function. It examines some cases in which Lohner's AWA algorithm must be suplimented by mathematical analysis.