Advanced Search

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 $\widehat{M}$. The usual semi-classical Trace formula expresses $Tr\left({\widehat{M}}^t\right)$ for finite time $t$, in the limit $\hslash \to 0$, in terms of periodic orbits of $M$ of period $t$. Recent work reach time $t\ll t_E/6$ where $t_E=log(1/\hslash )/\lambda$ is the Ehrenfest time, and $\lambda$ is the Lyapounov coefficient. Using a semi-classical normal form...