Complex Periodic Orbits and Tunnelling in Chaotic Potentials

Details Complex Periodic Orbits and Tunnelling in Chaotic Potentials Complex Periodic Orbits and Tunnelling in Chaotic Potentials

1996-08-03

arxiv.org/abs/chao-dyn/9608002v1

Phys. Rev. Lett. vol. 77, 4975 (1996).

Nonlinear Sciences

Chaotic Dynamics

Scientific paper

10.1103/PhysRevLett.77.4975

We derive a trace formula for the splitting-weighted density of states suitable for chaotic potentials with isolated symmetric wells. This formula is based on complex orbits which tunnel through classically forbidden barriers. The theory is applicable whenever the tunnelling is dominated by isolated orbits, a situation which applies to chaotic systems but also to certain near-integrable ones. It is used to analyse a specific two-dimensional potential with chaotic dynamics. Mean behaviour of the splittings is predicted by an orbit with imaginary action. Oscillations around this mean are obtained from a collection of related orbits whose actions have nonzero real part.

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