Dresden 2011 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 15: ISPS Intersectional Poster Session

DY 15.14: Poster

Dienstag, 15. März 2011, 18:00–20:00, P1

Power–Law Level–Statistics due to Dynamical Tunneling — Arnd Bäcker^1,2, Roland Ketzmerick^1,2, Steffen Löck¹, and •Normann Mertig¹ — ¹Institut für Theoretische Physik, Technische Universität Dresden, 01062 Dresden — ²MPI für Physik komplexer Systeme, 01187 Dresden

For systems with a mixed phase space we demonstrate that dynamical tunneling universally leads to a fractional power-law of the nearest-neighbor level-spacing distribution P(s) at small spacings s. Going beyond Berry-Robnik statistics, we take into account that dynamical tunneling rates between the regular and the chaotic region vary over many orders of magnitude. This results in a prediction of the level-spacing distribution which excellently describes the spectral data of the standard map. Moreover, we show that the fractional power-law exponent is proportional to the effective Planck constant h and discuss the emergence of Berry-Robnik statistics in the semiclassical limit h→ 0.