WKB Theory of Tunneling between Tori
Shoji Takada, Hiroki Nakamura
General WKB theory of multidimensional tunneling between tori is formulated and illuminating physical picture on the effects of multidimensionality is provided. On the basis of Wilkinson's work, (1) Maslov's semiclassical wavefunction in classically accessible region is connected to the wavefunction in classically inaccessible region and (2) the latter is propagated into deep tunneling region. It is found that there exist two distinct regions of tunneling : a region where action is pure imaginary (I-region) and another region where action is complex (C-region). In I-region tunneling path can be defined by a certain classical trajectory on the inverted potential, while in C-region no tunneling path can be defined and the Huygens type wave propagation should be carried out. Moreover, wavefunction of a vibrationally excited state has nodal lines in C-region but not in I-region.
Progress of Theoretical Physics Supplement•Feb 1, 1994•3 citations