From quantum scattering resonances to Pollicott-Ruelle resonances
(by Pierre Gaspard)
The quantum scattering resonances control the decay of the quantum-mechanical wave packets
and they are defined as complex energies. In contrast, the Pollicott-Ruelle resonances
control the decay of the statistical correlation functions in classical
dynamical systems theory and they are defined as complex frequencies. Typically, frequencies
(such as the Bohr frequencies)
are given by differences between two energies divided by hbar.
In the context of quantum systems, the concept of Pollicott-Ruelle resonance emerges in the
quasi-classical limit and they describe the collective effect of many quantum scattering
resonances. The connection between both types of resonances is explained and illustrated by
applications to molecular reactions, billiards, and quantum graphs.