Takahashi Kin'ya, Ikeda Kensuke S
The Physics Laboratories, Kyushu Institute of Technology, Kawazu 680-4, Iizuka 820-8502, Japan.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Nov;86(5 Pt 2):056206. doi: 10.1103/PhysRevE.86.056206. Epub 2012 Nov 13.
In multidimensional barrier tunneling, there exist two different types of tunneling mechanisms, instanton-type tunneling and noninstanton tunneling. In this paper we investigate transitions between the two tunneling mechanisms from the semiclassical and quantum viewpoints taking two simple models: a periodically perturbed Eckart barrier for the semiclassical analysis and a periodically perturbed rectangular barrier for the quantum analysis. As a result, similar transitions are observed with change of the perturbation frequency ω for both systems, and we obtain a comprehensive scenario from both semiclassical and quantum viewpoints for them. In the middle range of ω, in which the plateau spectrum is observed, noninstanton tunneling dominates the tunneling process, and the tunneling amplitude takes the maximum value. Noninstanton tunneling explained by stable-unstable manifold guided tunneling (SUMGT) from the semiclassical viewpoint is interpreted as multiphoton-assisted tunneling from the quantum viewpoint. However, in the limit ω→0, instanton-type tunneling takes the place of noninstanton tunneling, and the tunneling amplitude converges on a constant value depending on the perturbation strength. The spectrum localized around the input energy is observed, and there is a scaling law with respect to the width of the spectrum envelope, i.e., the width ∝ℏω. In the limit ω→∞, the tunneling amplitude converges on that of the unperturbed system, i.e., the instanton of the unperturbed system.
在多维势垒隧穿中，存在两种不同类型的隧穿机制，即瞬子型隧穿和非瞬子隧穿。在本文中，我们从半经典和量子观点出发，通过两个简单模型研究这两种隧穿机制之间的转变：用于半经典分析的周期性微扰埃卡特势垒和用于量子分析的周期性微扰矩形势垒。结果表明，对于这两个系统，随着微扰频率ω的变化都观察到了类似的转变，并且我们从半经典和量子观点出发得到了关于它们的全面图景。在观察到平台谱的ω的中间范围内，非瞬子隧穿主导隧穿过程，并且隧穿振幅取最大值。从半经典观点由稳定 - 不稳定流形引导隧穿（SUMGT）解释的非瞬子隧穿，从量子观点被解释为多光子辅助隧穿。然而，在ω→0的极限情况下，瞬子型隧穿取代了非瞬子隧穿，并且隧穿振幅收敛到一个取决于微扰强度的常数。观察到围绕输入能量局域化的谱，并且关于谱包络的宽度存在一个标度律，即宽度∝ℏω。在ω→∞的极限情况下，隧穿振幅收敛到未微扰系统的振幅，即未微扰系统的瞬子。
