MODEL TUNNELING PROBLEMS IN A HIGH MAGNETIC-FIELD
MODEL TUNNELING PROBLEMS IN A HIGH MAGNETIC-FIELD
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DOI：
10.1103/physrevb.37.4111
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发表时间：
1988-03-15
影响因子：
3.7
通讯作者：
KIVELSON, S
中科院分区：
文献类型：
--
作者：
JAIN, JK;KIVELSON, S
我们通过Schrödinger方程的数值积分和路径积分的半经典计算，研究了在高横向磁场存在下的二维简单隧道问题。我们选择了三种模型电位：(i)非对称单井，（ii）对称双井和（iii）四层井。我们发现半经典方法是解析上易于处理的，并且对隧穿矩阵元素的指数和振荡行为给出了非常准确的描述。给出了隧道路径的Aharonov-Bohm相位的精确定义。除了Aharonov-Bohm相位外，还有一个来自波动行列式的几何相位，我们发现对于每个闭环，它都恰好是±π。
We have studied simple tunneling problems in two dimensions in the presence of a high transverse magnetic field both by numerical integration of the Schrödinger equation and by semiclassical evaluation of the path integral. We have chosen three model potentials:(i) asymmetric single well,(ii) symmetric double well, and (iii) quadruple well. We find that the semiclassical approach is analytically tractable and gives a very accurate description of the exponential and oscillatory behaviors of the tunneling matrix elements. A precise definition of the Aharonov-Bohm phase for the tunneling paths is given. In addition to the Aharonov-Bohm phase, there is also a geometrical phase coming from the fluctuation determinant, and we find that for every closed loop it is exactly±π.