Heidelberg 1999 – scientific programme

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MP: Theoretische und Mathematische Grundlagen der Physik

MP 7: Endliche Quantensysteme und Quantenchaos

MP 7.2: Fachvortrag

Thursday, March 18, 1999, 16:20–16:40, MA1

Maximum norms of chaotic quantum eigenstates and random waves — •Roman Schubert, Ralf Aurich, Arnd Bäcker, and Michael Taglieber — Abteilung Theoretische Physik, Universität Ulm

The growth of the maximum norms of quantum eigenstates of classically chaotic systems with increasing energy is investigated. The maximum norms provide a measure for localization effects in eigenfunctions. An upper bound for the maxima of random superpositions of random functions is derived. For the random-wave model this gives the bound c √lnE in the semiclassical limit E→ ∞. The growth of the maximum norms of random waves is compared with the growth of the maximum norms of the eigenstates of six quantum billiards which are classically chaotic. The maximum norms of these systems are numerically shown to be conform with the random-wave model. Furthermore, the distribution of the locations of the maximum norms is discussed.

[1] R. Aurich, A. Bäcker, R. Schubert and M. Taglieber: Maximum norms of chaotic quantum eigenstates and random waves, Ulm Report ULM-TP/98-1 (available at http://www.physik.uni-ulm.de/theo/qc/), to appear in Physica D.