Tunneling paths in multi-dimensional semiclassical dynamics
Tunneling paths in multi-dimensional semiclassical dynamics
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多维半经典动力学中的隧道路径
DOI：
10.1016/s0370-1573(99)00036-8
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发表时间：
1999
期刊：
影响因子：
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通讯作者：
A. Inoue
中科院分区：
文献类型：
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作者：
K. Takatsuka;H. Ushiyama;A. Inoue
鉴于隧道现象的重要性和新的研究兴趣，我们回顾了半经典隧道理论的最新发展，特别是从“隧道路径”的观点出发，从简单的一维公式到利用时间、坐标或动量的解析延拓的半经典理论，这些解析延拓是Feynman路径积分的半经典近似的定态解。我们还特别注意瞬子路径，并介绍各种传统的和/或直观的想法来产生隧道路径，其中一维隧道理论的应用。然后，我们回顾了基于Hamilton-Jacobi方程的广义经典力学的最新进展，其中普通牛顿解和瞬子路径都被视为特例。这些新的复值解是沿着位形空间中的实值路径沿着生成的。这种非牛顿力学是根据一个称为“运动宇称”的量引入的。作为隧穿中的多体效应，本文主要以汉密尔顿混沌和化学反应动力学为背景，给出了一些说明性的数值例子，显示了多维隧穿是如何受到系统参数如质量组合和势函数各向异性的影响。
In light of the fundamental importance and renewed interest of the tunnel phenomena, we review the recent development of semiclassical tunneling theory, particularly from the view point of “tunneling path”, beginning from a simple one-dimensional formula to semiclassical theories making use of the analytic continuation, in time, coordinates, or momentum, which are the stationary solutions of semiclassical approximations to the Feynman path integrals. We also pay special attention to the instanton path and introduce various conventional and/or intuitive ideas to generate tunneling paths, to which one-dimensional tunneling theory is applied. Then, we review the recent progress in generalized classical mechanics based on the Hamilton–Jacobi equation, in which both the ordinary Newtonian solutions and the instanton paths are regarded as just special cases. Those new complex-valued solutions are generated along real-valued paths in configuration space. Such non-Newtonian mechanics is introduced in terms of a quantity called “parity of motion”. As many-body effects in tunneling, illustrative numerical examples are presented mainly in the context of the Hamilton chaos and chemical reaction dynamics, showing how the multidimensional tunneling is affected by the system parameters such as mass combination and anisotropy of potential functions.
S.Takada：“振动激励对多维隧道效应的影响：托酚酮中的一般研究和质子隧道效应”J.Chem.Phys.（印刷中）。
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