Lee Ming-Jer, Antonsen Thomas M, Ott Edward, Pecora Louis M
University of Maryland, College Park, Maryland 20742, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Nov;86(5 Pt 2):056212. doi: 10.1103/PhysRevE.86.056212. Epub 2012 Nov 21.
Recent numerical experiments of Pecora et al. [Phys. Rev. E 83, 065201 (2011)] have investigated tunneling between two-dimensional symmetric double wells separated by a tunneling barrier. The wells were bounded by hard walls and by the potential barrier which was created by a step increase from the zero potential within a well to a uniform barrier potential within the barrier region, which is a situation potentially realizable in the context of quantum dots. Numerical results for the splitting of energy levels between symmetric and antisymmetric eigenstates were calculated. It was found that the splittings vary erratically from state to state, and the statistics of these variations were studied for different well shapes with the fluctuation levels being much less in chaotic wells than in comparable nonchaotic wells. Here we develop a quantitative theory for the statistics of the energy level splittings for chaotic wells. Our theory is based on the random plane wave hypothesis of Berry. While the fluctuation statistics are very different for chaotic and nonchaotic well dynamics, we show that the mean splittings of differently shaped wells, including integrable and chaotic wells, are the same if their well areas and barrier parameters are the same. We also consider the case of tunneling from a single well into a region with outgoing quantum waves.
佩科拉等人[《物理评论E》83, 065201 (2011)]最近的数值实验研究了由隧穿势垒分隔的二维对称双阱之间的隧穿。阱由硬壁以及势垒界定，该势垒是通过从阱内的零势阶跃增加到势垒区域内的均匀势垒势而产生的，这是在量子点背景下可能实现的一种情况。计算了对称和反对称本征态之间能级分裂的数值结果。发现分裂在不同状态之间变化不规则，并且针对不同阱形状研究了这些变化的统计特性，混沌阱中的波动水平比可比的非混沌阱中的波动水平小得多。在这里，我们为混沌阱的能级分裂统计特性建立了一种定量理论。我们的理论基于贝里的随机平面波假设。虽然混沌和非混沌阱动力学的波动统计特性非常不同，但我们表明，如果不同形状的阱（包括可积阱和混沌阱）的阱面积和势垒参数相同，它们的平均分裂是相同的。我们还考虑了从单个阱隧穿到具有出射量子波的区域的情况。
