Tunneling and Chaos

Abstract

Over the preceeding twenty years, the role of underlying classical dynamics in quantum mechanical tunneling has received considerable attention. A number of new tunneling phenomena have been uncovered that have been directly linked to the set of dynamical possibilities arising in simple systems that contain at least some chaotic motion. These tunneling phenomena can be identified by their novel $\hslash$-dependencies and/or statistical behaviors. We summarize a sampling of these phenomena and mention some applications.

Review article for Nobel Symposium entitled `Quantum Chaos Y2K', no figures

References in corpus (1)

• New Class of Eigenstates in Generic Hamiltonian Systems

Cited by in corpus (5)

• Dynamical tunneling in molecules: Quantum routes to energy flow
• Signatures of unstable semiclassical trajectories in tunneling
• Mixed eigenstates in the Dicke model: Statistics and power-law decay of the relative proportion in the semiclassical limit
• Power-law decay of the fraction of the mixed eigenstates in kicked top model with mixed-type classical phase space
• Long quantum transition times due to unstable semiclassical dynamics