Semi-classical formula beyond the Ehrenfest time in quantum chaos. (I) Trace formula
| dc.creator | Faure, Frederic | |
| dc.date | 2006-10-03 | |
| dc.date | 2007-03-19 | |
| dc.date.accessioned | 2026-07-07T13:13:12Z | |
| dc.date.available | 2026-07-07T13:13:12Z | |
| dc.description | We consider a nonlinear area preserving Anosov map M on the torus phase space, which is the simplest example of a fully chaotic dynamics. We are interested in the quantum dynamics for long time, generated by the unitary quantum propagator Mq. The usual semi-classical Trace formula expresses Tr(Mq^t) for finite time t, in the limit hbar->0, in terms of periodic orbits of M of period t. Recent work reach time t<< tE/6 where tE=log(1/hbar)/lambda is the Ehrenfest time, and lambda is the Lyapounov coefficient. Using a semi-classical normal form description of the dynamics uniformly over phase space, we show how to extend the trace formula for longer time of the form t= C.tE where C is any constant, with an arbitrary small error. | |
| dc.description | 55 pages | |
| dc.identifier | https://arxiv.org/abs/nlin/0610004 | |
| dc.identifier | http://arxiv.org/abs/nlin/0610004 | |
| dc.identifier | Annales de l'Institut Fourier, Vol. 57 No.7, p. 2525-2599 (2007) | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/229813 | |
| dc.subject | Chaotic Dynamics | |
| dc.title | Semi-classical formula beyond the Ehrenfest time in quantum chaos. (I) Trace formula | |
| dc.type | text |