Regensburg 2007 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 12: Statistical physics (general)

DY 12.1: Talk

Tuesday, March 27, 2007, 10:00–10:15, H3

Energy correlations for a random matrix model of disordered bosons — •Tobias Lück¹, Hans-Jürgen Sommers², and Martin Zirnbauer¹ — ¹Institut für Theoretische Physik, Universität zu Köln, Zülpicher Straße 77, 50937 Köln, Germany — ²Fachbereich Physik, Universität Duisburg-Essen, Campus Essen, 45117 Essen, Germany

Linearizing the equations of motion around the ground state of an interacting quantum many-body system, one gets a time-evolution generator in the positive cone of a real symplectic Lie algebra. The presence of disorder in the physical system determines a probability measure with support on this cone. We analyzed a discrete family of such measures of exponential type using a simple random matrix model. Some generic statistical features of the characteristic frequencies of disordered bosonic quasi-particle systems can be derived. The level correlation functions of the said measures are shown to be those of a determinantal process, and the kernel of the process is expressed as a sum of bi-orthogonal polynomials. While the correlations in the bulk scaling limit are in accord with sine-kernel or GUE universality, at the low-frequency end of the spectrum an unusual type of scaling behavior is found.