Introduction

Abstract

A semiclassical description of tunneling in systems with complex dynamics requires an arsenal of theoretical techniques adapted to the problem under investigation. Conceptually, two types of processes are usually distinguished, namely, coherent and incoherent tunneling. The former one appears in biand multistable potentials and, more precisely, should be termed quantum coherence. It originates from the coherent overlap of wave functions located in individual domains, which are separated by energy or phase-space barriers. The latter one describes the situation, where in the language of scattering theory asymptotic states in the distant past do not overlap in the distant future with those that have penetrated a barrier. Accordingly, incoherent tunneling is seen in scattering processes between two reservoirs and in the decay of metastable states into a continuum. However, in presence of interaction with environmental degrees of freedom coherent tunneling dynamics can be destroyed leading to relaxation via incoherent decay as well.