%0 Book Section %1 statphys23_1015 %A Heusler, S. %A Mueller, S. %A Altland, A. %A Braun, P. %A Haake, F. %B Abstract Book of the XXIII IUPAP International Conference on Statistical Physics %C Genova, Italy %D 2007 %E Pietronero, Luciano %E Loreto, Vittorio %E Zapperi, Stefano %K chaotic classically correlation orbit periodic rmt spectral statphys23 topic-8 %T Periodic Orbit Theory of Level Correlation %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=1015 %X It was established some 20 years ago that statistical properties of the energy spectra of classically chaotic systems are universal and obey the Random Matrix Theory (RMT) predictions. We present a semiclassical explanation of this fact representing the spectral correlation functions as sums over sets of classical periodic orbits. We show that the relevant sets are composed of the so called partner orbits built of practically the same pieces traversed in different order and with different sense. Switching to another partner is done by reconnections within the orbit encounters, i.e., places where several stretches of the same orbit or different orbits are very close and almost parallel to each other. The existence of bunches of periodic orbit-partners is a striking feature of hyperbolic motion in classical mechanics. After summation over all sets of partner orbits the exact RMT spectral correlation functions are reproduced.

@incollection{statphys23_1015, abstract = {It was established some 20 years ago that statistical properties of the energy spectra of classically chaotic systems are universal and obey the Random Matrix Theory (RMT) predictions. We present a semiclassical explanation of this fact representing the spectral correlation functions as sums over sets of classical periodic orbits. We show that the relevant sets are composed of the so called partner orbits built of practically the same pieces traversed in different order and with different sense. Switching to another partner is done by reconnections within the orbit encounters, i.e., places where several stretches of the same orbit or different orbits are very close and almost parallel to each other. The existence of bunches of periodic orbit-partners is a striking feature of hyperbolic motion in classical mechanics. After summation over all sets of partner orbits the exact RMT spectral correlation functions are reproduced.}, added-at = {2007-06-20T10:16:09.000+0200}, address = {Genova, Italy}, author = {Heusler, S. and Mueller, S. and Altland, A. and Braun, P. and Haake, F.}, biburl = {https://www.bibsonomy.org/bibtex/25da8291b7c600893812a5329467fb0f5/statphys23}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {8aac2aa2c58430748fd8a37dad0b2ac4}, intrahash = {5da8291b7c600893812a5329467fb0f5}, keywords = {chaotic classically correlation orbit periodic rmt spectral statphys23 topic-8}, month = {9-13 July}, timestamp = {2007-06-20T10:16:36.000+0200}, title = {Periodic Orbit Theory of Level Correlation}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=1015}, year = 2007 }