Instanton trajectory, multidimensional tunneling

The theory developed for tunneling splitting can be easily extended to the decay of the metastable state through multidimensional tunneling, namely, tunneling predissociation of polyatomic molecules. In the case of predissociation, however, the instanton trajectory cannot be fixed at both ends, but one end should be free (see Fig. 17). The boundary conditions are... 

In particular, the high-temperature regime T>TC, where the trivial trajectory jc(t) = x is the only solution contributing to Im F, is correctly described by the instanton formalism. Furthermore, the equivalence of (2.6) (at T = 0) and (3.68) for the cubic parabola is demonstrated in Appendix B. Although at first the infinite determinants in (3.67) might look less attractive than simple formulas (2.6) and (2.7) or the direct WKB solution by Schmid, it is the instanton approach that permits direct generalization to dissipative tunneling and to the multidimensional problem. 

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