Analytic Perturbation Theory and Renormalization Analysis of Matter Coupled to Quantized Radiation

For a large class of quantum mechanical models of matter and radiation we develop an analytic perturbation theory for non-degenerate ground states. This theory is applicable, for example, to models of matter with static nuclei and non-relativistic electrons that are coupled to the UV-cutoff quantized radiation field in the dipole approximation. If the lowest point of the energy spectrum is a non-degenerate eigenvalue of the Hamiltonian, we show that this eigenvalue is an analytic function of the nuclear coordinates and of $\alpha^{3/2}$, $\alpha$ being the fine structure constant. A suitably chosen ground state vector depends analytically on $\alpha^{3/2}$ and it is twice continuously differentiable with respect to the nuclear coordinates.Comment: 47 page

A vanishing theorem for operators in Fock space

We consider the bosonic Fock space over the Hilbert space of transversal vector fields in three dimensions. This space carries a canonical representation of the group of rotations. For a certain class of operators in Fock space we show that rotation invariance implies the absence of terms which either create or annihilate only a single particle. We outline an application of this result in an operator theoretic renormalization analysis of Hamilton operators, which occur in non-relativistic qed.Comment: 14 page

Ranking News-Quality Multimedia

News editors need to find the photos that best illustrate a news piece and fulfill news-media quality standards, while being pressed to also find the most recent photos of live events. Recently, it became common to use social-media content in the context of news media for its unique value in terms of immediacy and quality. Consequently, the amount of images to be considered and filtered through is now too much to be handled by a person. To aid the news editor in this process, we propose a framework designed to deliver high-quality, news-press type photos to the user. The framework, composed of two parts, is based on a ranking algorithm tuned to rank professional media highly and a visual SPAM detection module designed to filter-out low-quality media. The core ranking algorithm is leveraged by aesthetic, social and deep-learning semantic features. Evaluation showed that the proposed framework is effective at finding high-quality photos (true-positive rate) achieving a retrieval MAP of 64.5% and a classification precision of 70%.Comment: To appear in ICMR'1

Ground state properties in non-relativistic QED

We discuss recent results concerning the ground state of non-relativistic quantum electrodynamics as a function of a magnetic coupling constant or the fine structure constant, obtained by the authors in [12,13,14].Comment: 6 Pages, contribution to the Proceedings of the Conference QMath 11 held in Hradec Kralove (Czechia) in September 201

Anderson Localization at Band Edges for Random Magnetic Fields

We consider a magnetic Schr\"odinger operator in two dimensions. The magnetic field is given as the sum of a large and constant magnetic field and a random magnetic field. Moreover, we allow for an additional deterministic potential as well as a magnetic field which are both periodic. We show that the spectrum of this operator is contained in broadened bands around the Landau levels and that the edges of these bands consist of pure point spectrum with exponentially decaying eigenfunctions. The proof is based on a recent Wegner estimate obtained in \cite{EH2} and a multiscale analysis