Leipzig 2002 – scientific programme

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MP: Theoretische und Mathematische Grundlagen der Physik

MP 15: Quanten-Chaos

MP 15.1: Fachvortrag

Monday, March 18, 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.
T. Kottos and U. Smilansky, Phys. Rev. Lett. 79, 4794 (1997).
W. Bulla and T. Trenkler, J. Math. Phys. 31, 1157 (1990).