Jiri Vanicek
Dept of Chemistry, University of California, Berkeley.
| Scattering of linear waves can be very sensitive to small changes in the scattering environment. In the quantum context this can be quantified by the so-called 'fidelity': two initially identical waves are propagated in an unperturbed and a slightly perturbed environment, respectively. Fidelity is the overlap of the two waves at time t. It has been of recent theoretical interest to ask how this fidelity behaves when the underlying ray (classical) dynamics is chaotic. The wave problem is difficult to calculate numerically in the short-wavelength regime because of the exponentially growing number of classical trajectories. I present a semiclassical method making this possible and accurate even in situations with ~10^70 classical trajectories. This method can directly justify various regimes of fidelity decay ('perturbative', 'Fermi-Golden-Rule', and 'Lyapunov') observed in recent literature. I will discuss the extended validity of the classical perturbation theory and defend linear response theory from the famous Van Kampen objection. Finally, I will show how our method provides a bridge between the quantum Feynman propagator based on the path integral and the semiclassical Van Vleck propagator based on the sum over classical trajectories. |
Back to AML Seminar Schedule