Studies on Chaotic Tunneling

研究了多维隧道现象，重点研究了混沌现象。从复域半经典理论的角度对动力隧穿和势垒隧穿进行了广泛的研究。揭示了一种特征复化经典流形（我们称之为“Laputa链”）在相空间混沌和可积域间动力学隧穿的经典描述中起着重要作用。考虑到勒皮他链，我们发现半经典理论再现了隧穿波函数的每一个细节。我们还证明了Laputa链与复杂动力系统的核心概念Julia集密切相关。在势垒隧穿问题中，我们发现势垒的不稳定流形与输入光束表面之间的异斜纠缠起着至关重要的作用。这种效应极大地改变了在传统的多维隧穿理论中完全被忽视的能量势垒

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