Diagrammatic routes to nonlocal correlations beyond dynamical mean field theory

Strong electronic correlations pose one of the biggest challenges to solid state theory. We review recently developed methods that address this problem by starting with the local, eminently important correlations of dynamical mean field theory (DMFT). On top of this, non-local correlations on all length scales are generated through Feynman diagrams, with a local two-particle vertex instead of the bare Coulomb interaction as a building block. With these diagrammatic extensions of DMFT long-range charge-, magnetic-, and superconducting fluctuations as well as (quantum) criticality can be addressed in strongly correlated electron systems. We provide an overview of the successes and results achieved---hitherto mainly for model Hamiltonians---and outline future prospects for realistic material calculations.Comment: 60 pages, 42 figures, replaced by the version to be published in Rev. Mod. Phys. 201

Resonant Auger Effect at High X-Ray Intensity

The resonant Auger effect of atomic neon exposed to high-intensity x-ray radiation in resonance with the 1s {yields} 3p transition is discussed. High intensity here means that the x-ray peak intensity is sufficient ({approx} 10{sup 18} W/cm{sup 2}) to induce Rabi oscillations between the neon ground state and the 1s{sup -1}3p ({sup 1}P) state within the relaxation lifetime of the inner-shell vacancy. For the numerical analysis presented, an effective two-level model, including a description of the resonant Auger decay process, is employed. Both coherent and chaotic x-ray pulses are treated. The latter are used to simulate radiation from x-ray free-electron lasers based on the principle of self-amplified spontaneous emission. Observing x-ray-driven atomic population dynamics in the time domain is challenging for chaotic pulse ensembles. A more practical option for experiments using x-ray free-electron lasers is to measure the line profiles in the kinetic energy distribution of the resonant Auger electron. This provides information on both atomic population dynamics and x-ray pulse properties

Projection on higher Landau levels and non-commutative geometry

The projection of a two dimensional planar system on the higher Landau levels of an external magnetic field is formulated in the language of the non commutative plane and leads to a new class of star products.Comment: 12 pages, latex, corrected versio