Ishikawa Akiyuki, Tanaka Atushi, Shudo Akira
Department of Physics, Tokyo Metropolitan University, Tokyo, Japan.
Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Oct;80(4 Pt 2):046204. doi: 10.1103/PhysRevE.80.046204. Epub 2009 Oct 6.
Quantum tunneling in the presence of chaos is analyzed, focusing especially on the interplay between quantum tunneling and dynamical localization. We observed flooding of potentially existing tunneling amplitude by adding noise to the chaotic sea to attenuate the destructive interference generating dynamical localization. This phenomenon is related to the nature of complex orbits describing tunneling between torus and chaotic regions. The tunneling rate is found to obey a perturbative scaling with noise intensity when the noise intensity is sufficiently small and then saturate in a large noise intensity regime. A relation between the tunneling rate and the localization length of the chaotic states is also demonstrated. It is shown that due to the competition between dynamical tunneling and dynamical localization, the tunneling rate is not a monotonically increasing function of Planck's constant. The above results are obtained for a system with a sharp border between torus and chaotic regions. The validity of the results for a system with a smoothed border is also explained.
分析了存在混沌时的量子隧穿，特别关注量子隧穿与动态局域化之间的相互作用。我们通过向混沌海中添加噪声来减弱产生动态局域化的相消干涉，从而观察到潜在存在的隧穿振幅的泛滥。这种现象与描述环面和混沌区域之间隧穿的复杂轨道的性质有关。当噪声强度足够小时，发现隧穿率服从与噪声强度的微扰标度关系，然后在大噪声强度 regime 中达到饱和。还证明了隧穿率与混沌态的局域化长度之间的关系。结果表明，由于动态隧穿和动态局域化之间的竞争，隧穿率不是普朗克常数的单调递增函数。上述结果是针对环面和混沌区域之间具有清晰边界的系统获得的。还解释了对于具有平滑边界的系统结果的有效性。
