Studies on Chaotic Tunneling

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Multi-dimensional tunneling phenomena is studied putting particular emphasis on chaotic phenomena. Dynamical tunneling and barrier tunneling are investigated extensively in terms of complex-domain semiclassical theory.It reveals that a characteristic complexified classical manifold which we call "Laputa chain" plays a crucial role in the classical description of dynamical tunneling among chaotic and inte-grable domains of the phase space. Taking into Laputa chains, we found that the semiclassical theory reproduces every detail of tunneling wave function. We also showed that the Laputa chain is closely related with the Julia sets, which is a central concept of complex dynamical systems.In the barrier tunneling problem, we discovered that the heteroclinic entanglement between the unstable manifold of the tunneling barrier and the input beam surface plays a crucial role. Such an effect drastically changes the multi-dimensional tunneling through the energy barrier which has completely been overlooked in the traditional theory of multi-dimensional tunneling