Münster 1999 – scientific programme

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DY: Dynamik und Statistische Physik

DY 44: Quantenchaos I

DY 44.5: Talk

Thursday, March 25, 1999, 15:45–16:00, R4

Spectral Statistics: From Eigenphases to Energies — •Rafael Mendez^1,2, Thomas Seligman³, Francois Leyvraz³, and M. Lombardi⁴ — ¹Fachbereich 7 Physik, GH Essen University, 45117 — ²Permanent Address: Centro de Ciencias Físicas, UNAM — ³Centro de Ciencias Físicas, Universidad Nacional Autónoma de México — ⁴Laboratoire de Spectrometrie Physique-Univeristé J. Fourier de Grenoble, France

We show that, given hamiltonian whose classical analog is completely chaotic, it is possible to transfer the statistical properties of the eigenphases of its associated quantum Poincaré map to those of the energies of the original hamiltonian. In the completely chaotic case we obtain that the fluctuation properties of the eigenphases of the the quantum Poincaré map will be those of the circular ensembles with probability one. We show later that the local fluctuation properties of the energy spectra are the same as those predicted by the gaussian ensembles with probability one, a result known as the Bohigas-Giannoni-Schmit conjecture. This is verified in two examples, one in billiards and the other in Rydberg molecules. In the latter we furthermore show that the multichannel quantum defect theory (MQDT) can be interpreted as a quantum Poincaré map, with is unitary by construction.