Browsing by Author "Kirsch, Werner"
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- ItemCorrelations and Interactions for Random Quantum Systems(Zürich : EMS Publ. House, 2011) Kirsch, Werner; Müller, Peter; Warzel, SimoneRandom quantum systems cover a broad range of mathematical models from random Schr¨odinger operators to random matrices and quantum spin models with random parameters. Their understanding requires techniques which combine functional analysis and probability. The workshop brought together researchers from these various branches which discussed new results, methods and future challenges. This is a report on the meeting containing extended abstracts of the lectures.
- ItemDisordered Systems: Random Schrödinger Operators and Random Matrices(Zürich : EMS Publ. House, 2008) Kirsch, Werner; Klopp, Frederic; Kriecherbauer, Thomas[no abstract available]
- ItemMathematics and Physics of Disordered Systems(Zürich : EMS Publ. House, 2004) Kirsch, Werner; Leschke, Hajo; Pastur, Leonid[no abstract available]
- ItemRandom block operators(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2010) Kirsch, Werner; Metzger, Bernd; Müller, PeterWe study fundamental spectral properties of random block operators that are common in the physical modelling of mesoscopic disordered systems such as dirty superconductors. Our results include ergodic properties, the location of the spectrum, existence and regularity of the integrated density of states, as well as Lifshits tails. Special attention is paid to the peculiarities arising from the block structure such as the occurrence of a robust gap in the middle of the spectrum. Without randomness in the off-diagonal blocks the density of states typically exhibits an inverse square-root singularity at the edges of the gap. In the presence of randomness we establish a Wegner estimate that is valid at all energies. It implies that the singularities are smeared out by randomness, and the density of states is bounded. We also show Lifshits tails at these band edges. Technically, one has to cope with a non-monotone dependence on the random couplings