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8 papers · 1 filter
Positive commutators, Fermi golden rule and the spectrum of zero temperature Pauli-Fierz Hamiltonians
Sylvain Golénia
We perform the spectral analysis of a zero temperature Pauli-Fierz system for small coupling constants. Under the hypothesis of Fermi golden rule, we show that the embedded eigenva…
The Non-Trapping Degree of Scattering
Andreas Knauf, Markus Krapf
We consider classical potential scattering. If no orbit is trapped at energy E, the Hamiltonian dynamics defines an integer-valued topological degree. This can be calculated explic…
Scaling diagram for the localization length at a band edge
Christian Sadel, Hermann Schulz-Baldes
A weak-coupling scaling diagram for the Lyapunov exponent and the integrated density of states near a band edge of a random Jacobi matrix is obtained. The analysis is based on the…
Gaussian fluctuations for random matrices with correlated entries
Jeffrey Schenker, Hermann Schulz-Baldes
For random matrix ensembles with non-gaussian matrix elements that may exhibit some correlations, it is shown that centered traces of polynomials in the matrix converge in distribu…
Energetic and dynamic properties of a quantum particle in a spatially random magnetic field with constant correlations along one direction
Hajo Leschke, Simone Warzel, Alexandra Weichlein
We consider an electrically charged particle on the Euclidean plane subjected to a perpendicular magnetic field which depends only on one of the two Cartesian co-ordinates. For suc…
Semicircle law and freeness for random matrices with symmetries or correlations
Jeffrey H. Schenker, Hermann Schulz-Baldes
For a class of random matrix ensembles with correlated matrix elements, it is shown that the density of states is given by the Wigner semi-circle law. This is applied to effective…