Hamburg 2001 – scientific programme

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SYGS: 30 Jahre Gutzwiller Spurformel

SYGS IV: HV IV

SYGS IV.1: Invited Talk

Wednesday, March 28, 2001, 16:00–16:30, S6

Semiclassics Beyond the Diagonal Approximation: Spectral Statistics and Quantum Transport — •Klaus Richter and Martin Sieber — Max-Planck-Institut für Physik komplexer Systeme, Dresden

The trace formula allows for the most direct link between spectral statistics of a complex quantum system and its chaotic classical dynamics. However, there exists the outstanding problem to evaluate double sums over infinitely many classical paths, appearing in a semiclassical treatment, in order to derive random matrix predictions for the energy level statistics. We believe that subtle correlations between periodic orbits play a key role and show how to obtain corrections to Berry’s “diagonal approximation”, in agreement with random matrix theory [1]. This problem is closely related to the long-lasting question to compute semiclassically quantum corrections to the classical conductance in ballistic mesoscopic systems in a quantitative way.

[1] M. Sieber and K. Richter, Physica Scripta, in press (2001)