Tunneling paths in multidimensional semiclassical dynamics
Abstract
In light of the fundamental importance and renewed interest of the tunnel phenomena, we review the recent development of semiclassical tunneling theory, particularly from the view point of “tunneling path”, beginning from a simple onedimensional formula to semiclassical theories making use of the analytic continuation, in time, coordinates, or momentum, which are the stationary solutions of semiclassical approximations to the Feynman path integrals. We also pay special attention to the instanton path and introduce various conventional and/or intuitive ideas to generate tunneling paths, to which onedimensional tunneling theory is applied. Then, we review the recent progress in generalized classical mechanics based on the HamiltonJacobi equation, in which both the ordinary Newtonian solutions and the instanton paths are regarded as just special cases. Those new complexvalued solutions are generated along realvalued paths in configuration space. Such nonNewtonian mechanics is introduced in terms of a quantity called “parity of motion”. As manybody 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 system parameters such as mass combination and anisotropy of potential functions.
 Publication:

Physics Reports
 Pub Date:
 December 1999
 DOI:
 10.1016/S03701573(99)000368
 Bibcode:
 1999PhR...322..347T