Wavefront sets in algebraic quantum field theory

The investigation of wavefront sets of n-point distributions in quantum field theory has recently acquired some attention stimulated by results obtained with the help of concepts from microlocal analysis in quantum field theory in curved spacetime. In the present paper, the notion of wavefront set of a distribution is generalized so as to be applicable to states and linear functionals on nets of operator algebras carrying a covariant action of the translation group in arbitrary dimension. In the case where one is given a quantum field theory in the operator algebraic framework, this generalized notion of wavefront set, called "asymptotic correlation spectrum", is further investigated and several of its properties for physical states are derived. We also investigate the connection between the asymptotic correlation spectrum of a physical state and the wavefront sets of the corresponding Wightman distributions if there is a Wightman field affiliated to the local operator algebras. Finally we present a new result (generalizing known facts) which shows that certain spacetime points must be contained in the singular supports of the 2n-point distributions of a non-trivial Wightman field.Comment: 34 pages, LaTex2

Structured random measurements in signal processing

Compressed sensing and its extensions have recently triggered interest in randomized signal acquisition. A key finding is that random measurements provide sparse signal reconstruction guarantees for efficient and stable algorithms with a minimal number of samples. While this was first shown for (unstructured) Gaussian random measurement matrices, applications require certain structure of the measurements leading to structured random measurement matrices. Near optimal recovery guarantees for such structured measurements have been developed over the past years in a variety of contexts. This article surveys the theory in three scenarios: compressed sensing (sparse recovery), low rank matrix recovery, and phaseless estimation. The random measurement matrices to be considered include random partial Fourier matrices, partial random circulant matrices (subsampled convolutions), matrix completion, and phase estimation from magnitudes of Fourier type measurements. The article concludes with a brief discussion of the mathematical techniques for the analysis of such structured random measurements.Comment: 22 pages, 2 figure

STM and RHEED study of the Si(001)-c(8x8) surface

The Si(001) surface deoxidized by short annealing at T~925C in the ultrahigh vacuum molecular beam epitaxy chamber has been in situ investigated by high resolution scanning tunnelling microscopy (STM) and reflected high energy electron diffraction (RHEED). RHEED patterns corresponding to (2x1) and (4x4) structures were observed during sample treatment. The (4x4) reconstruction arose at T<600C after annealing. The reconstruction was observed to be reversible: the (4x4) structure turned into the (2x1) one at T>600C, the (4x4) structure appeared again at recurring cooling. The c(8x8) reconstruction was revealed by STM at room temperature on the same samples. A fraction of the surface area covered by the c(8x8) structure decreased as the sample cooling rate was reduced. The (2x1) structure was observed on the surface free of the c(8x8) one. The c(8x8) structure has been evidenced to manifest itself as the (4x4) one in the RHEED patterns. A model of the c(8x8) structure formation has been built on the basis of the STM data. Origin of the high-order structure on the Si(001) surface and its connection with the epinucleation phenomenon are discussed.Comment: 26 pages, 12 figure

A New Derivation of the CPT and Spin-Statistics Theorems in Non-Commutative Field Theories

We propose an alternative axiomatic description for non-commutative field theories (NCFT) based on some ideas by Soloviev to nonlocal quantum fields. The local commutativity axiom is replaced by the weaker condition that the fields commute at sufficiently large spatial separations, called asymptotic commutativity, formulated in terms of the theory of analytic functionals. The question of a possible violation of the CPT and Spin-Statistics theorems caused by nonlocality of the commutation relations $[\hat{x}_\mu,\hat{x}_\nu]=i\theta_{\mu\nu}$ is investigated. In spite of this inherent nonlocality, we show that the modification aforementioned is sufficient to ensure the validity of these theorems for NCFT. We restrict ourselves to the simplest model of a scalar field in the case of only space-space non-commutativity.Comment: The title is new, and the analysis in the manuscript has been made more precise. This revised version is to be published in J.Math.Phy