Agenda

Since the early days of quantum mechanics, tunneling has been a fascinating and important subject. Though initially conceptualized in terms of energetic barriers, in the past 30 years or so, it has been recognized as a more general phenomenon in which a dynamical barrier plays the role of creating classically forbidden behavior. The quantitative understanding of dynamical tunneling in non-integrable systems, such as systems with regular and chaotic dynamics in a mixed phase space, still represents an open challenge in quantum physics.  Several semiclassical approaches to predict the level splittings, rates, and escape times that characterize tunneling processes in such non-integrable systems have been developed within the past two to three decades. They are often based on complex classical trajectories that penetrate the tunneling barrier, such as a complexification of the van-Vleck-Gutzwiller propagator, or on elementary classical properties of the dynamics with the well from which the tunneling process takes place, such as the depth of the well or presence of nonlinear resonances.

Some of our goals are:

1. Reconcile the theories of direct and resonance-assisted tunneling with the complexified van-Vleck-Gutzwiller propagator theory.

2. Better understand the ranges of applicability of such theories and their limitations.

3. Identify specific signatures that substructures in phase space imprint on tunneling phenomena and dominant classical trajectories.

4. Make progress on systems with greater than two degrees of freedom.

5. Consider whether better understanding of a unified theory of dynamical tunneling can be brought to bear on coherent control of tunneling processes.

 A focus event is planned for the week of June 14-17 to broaden the discussions and perspectives.