发表机构
Arizona State University; Shanghai Jiao Tong University; Stockholm University; KTH Royal Institute of Technology; Massachusetts Institute of Technology（亚利桑那州立大学; 上海交通大学; 斯德哥尔摩大学; 皇家理工学院; 麻省理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对薄势垒下作用量较小的隧穿问题，发展了以势垒下面积倒数为控制参数的微扰分析方法，在1+1维例子中得到共振/非共振隧穿概率随时间的不同增长规律，还计算了含时隧穿波函数。
AI 中文摘要
量子隧穿的常规WKB分析适用于隧穿作用量较大的情况，如高而宽的势垒。与之不同，本文分析作用量较小时的隧穿，即高而薄的势垒隧穿。我们发展了一种微扰分析方法，控制参数为势垒下面积的倒数，并将该技术应用于1+1维的多个例子中。对于束缚粒子的共振情况，我们发现隧穿概率随时间呈∝t²增长；非共振情况下则随时间线性增长。我们不仅计算了隧穿概率，还得到了逃逸至无穷远的粒子的含时隧穿波函数，即从准束缚态到连续态的波函数。
英文摘要
The usual WKB analysis for quantum tunneling applies when the tunneling action is large, as it is for tall, wide potential barriers. In contrast we analyze tunneling when the action is small, as it is for tunneling across a tall, thin barrier. We develop a perturbative analysis where the control parameter is the inverse of the area under the potential barrier and apply our technique to several examples in $1+1$ dimensions. In resonant situations for bound particles we find that the tunneling probability grows with time as $\propto t^2$, while in non-resonant situations it grows linearly with time. We evaluate not only the tunneling probability but also the time-dependent tunneling wavefunction for a particle that escapes to infinity, {\it i.e.} from a quasi-bound state to the continuum.
Comments14 pages, 9 figures; significant revisions in Secs. III.B, V.B and Appendix A
