Tunneling paths in multi-dimensional semiclassical dynamics

In light of the fundamental importance and renewed interest of the tunnel p henomena, we review the recent development of semiclassical tunneling theor y, particularly from the view point of "tunneling path" beginning from a si mple one-dimensional formula to semiclassical theories making use of the an alytic continuation, in time, coordinates, or momentum, which are the stati onary solutions of semiclassical approximations to the Feynman path integra ls. We also pay special attention to the instanton path and introduce vario us conventional and/or intuitive ideas to generate tunneling paths, to whic h one-dimensional tunneling theory is applied. Then, we review the recent p rogress in generalized classical mechanics based on the Hamilton-Jacobi equ ation, in which both the ordinary Newtonian solutions and the instanton pat hs are regarded as just special cases. Those new complex-valued solutions a re generated along real-valued paths in configuration space. Such non-Newto nian mechanics is introduced in terms of a quantity called "parity of motio n". As many-body effects in tunneling, illustrative numerical examples are presented mainly in the context of the Hamilton chaos and chemical reaction dynamics, showing how the multidimensional tunneling is affected by the sy stem parameters such as mass combination and anisotropy of potential functi ons. (C) 1999 Elsevier Science B.V. All rights reserved.