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DY: Fachverband Dynamik und Statistische Physik

DY 29: Quantum Chaos I

DY 29.9: Vortrag

Donnerstag, 17. März 2011, 12:15–12:30, ZEU 255

How long is the chaotic boundary of a billiard? — Arnd Bäcker^1,3, Roland Ketzmerick^1,3, •Steffen Löck¹, and Holger Schanz^2,3 — ¹Institut für Theoretische Physik, Technische Universität Dresden, 01062 Dresden — ²Institut für Maschinenbau, Hochschule Magdeburg-Stendal, 39114 Magdeburg — ³MPI für Physik komplexer Systeme, 01187 Dresden

For two-dimensional quantum billiards we derive a partial Weyl law, i.e. the average density of states for a subset of eigenstates concentrating on an invariant region Γ of phase space. The leading term is proportional to the area of the billiard times the phase-space fraction of Γ. The boundary term is proportional to the fraction of the boundary where parallel trajectories belong to Γ. Agreement with numerical data will be presented for the mushroom and the cosine billiard, where we determine the boundary lengths associated with chaotic and regular states, and for the elliptical billiard, where we consider rotating and oscillating states.