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We want to investigate quantum mechanical properties of 4D area preserving maps in the presence of nonlinear resonances. Therefore we will first focus on regular-to-chaotic tunneling rates for designed models without resonances and give a prediction using the fictitious integrable system approach developed for lower dimensional systems. Adding nonlinearities leads to prominent peaks in the tunneling rates γ vs. 1/h which we will explain qualitatively by an examination of the structure in the frequency plane. We will also visualize these resonances by sections through the 4D phase space which show complex regular regions interwoven with the Arnol’d web. |
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