Multidimensional systems barrier tunneling

The rate factors rr interrelate just two wells, the well 1 and the well r. For just one barrier separating the two wells, the classical path under the barrier does not split into branches. The classical path in the restricted area is approximately separable (see Section 5 later). Therefore, in JT systems, after the weight factors mr(r) are established, the multidimensional tunneling problem reduces to a one-dimensional consideration. 

The other important scenario in multidimensional tunneling is of the dynamical tunneling that is observed in 1.5D and 2D systems [21]. In this case, the classical phase space is separated not by the energy barrier but by the invariant surface (e.g., KAM tori). Such a situation is realized, for example, in periodically perturbed one-dimensional (1.5D) barrier potentials and also in 2D barrier systems when the total energy is taken over the potential saddle. In a series of recent articles [22-25], we have found a new class of tunneling phenomena... 

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