Leipzig 2002 – wissenschaftliches Programm

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MP: Theoretische und Mathematische Grundlagen der Physik

MP 15: Quanten-Chaos

MP 15.1: Fachvortrag

Montag, 18. März 2002, 17:00–17:12, SR 1033/34

The Dirac operator on graphs — •Jonathan Harrison and Jens Bolte — Abteilung Theoretische Physik, Universitat Ulm, Albert-Einstein-Allee 11, 89069 Ulm

The Schrödinger operator on graphs (networks of nodes connected by one dimensional bonds) has been used to provide a generic model of quantum systems which are classically chaotic [1]. By quantising the graphs using instead the Dirac operator [2] we obtain a model system for quantum chaos with spin. Results for this alternative representation of quantum chaos on a graph are compared to those obtained with the standard Schrödinger quantisation. A central problem is the determination of suitable boundary conditions for which the Dirac operator is self-adjoint and time reversal symmetric.
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