Tunnelling is examined from the point of view of analytic continuation of Lagrangian manifolds. This enables an intrinsically multidimensional approach to many problems. We illustrate the ideas by computing energy splittings between congruent tori in a number of integrable systems. The examples include an integrable but non-separable system which cannot be solved by reduction to one-dimensional systems. The calculations can all be viewed in a geometrical way that does not make explicit use of separation of coordinates.
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Stephen C. Creagh (1994) studied this question.
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