WENTZEL-KRAMERS-BRILLOUIN THEORY OF MULTIDIMENSIONAL TUNNELING - GENERAL-THEORY FOR ENERGY SPLITTING
WENTZEL-KRAMERS-BRILLOUIN THEORY OF MULTIDIMENSIONAL TUNNELING - GENERAL-THEORY FOR ENERGY SPLITTING
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DOI：
10.1063/1.466899
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发表时间：
1994-01-01
影响因子：
4.4
通讯作者：
NAKAMURA, H
中科院分区：
文献类型：
--
作者：
TAKADA, S;NAKAMURA, H
一个通用的Wentzel-Kramers-Brillouin（WKB）理论的多维隧道制定和照明物理图片的多维性的影响提供。解决了两个基本问题：（i）Maslov的半经典波函数在经典可达区域连接到经典不可达区域的波函数和（ii）后者传播到深隧穿区域。发现存在两种不同类型的隧穿：纯隧穿和混合隧穿。前者是通常的一种，其中隧穿路径可以由倒势上的某个经典轨迹来定义，其相关作用是纯虚的。在后一种情况下，没有隧道路径可以被定义和惠更斯型波传播应该进行。在这种情况下，隧穿总是伴随着经典运动的横向方向和相关的行动是复杂的。给出了计算双势阱中能量分裂Δ E的一般方法。在局部可分线性近似下，导出了一个简便的DELTAE计算公式，并与精确数值计算结果进行了比较。
A general Wentzel-Kramers-Brillouin (WKB) theory of multidimensional tunneling is formulated and an illuminating physical picture of the effects of multidimensionality is provided. Two basic problems are solved: (i) Maslov's semiclassical wave function in the classically accessible region is connected to the wave function in the classically inaccessible region and (ii) the latter is propagated into the deep tunneling region. It is found that there exist two distinct types of tunneling: pure tunneling and mixed tunneling. The former is the usual one in which the tunneling path can be defined by a certain classical trajectory on the inverted potential and its associated action is pure imaginary. In the latter case, no tunneling path can be defined and the Huygens-type wave propagation should be carried out. In this case, tunneling is always accompanied by classical motion in the transversal direction and the associated action is complex. A general procedure is presented for the evaluation of energy splitting DELTAE in the double well. Moreover, under the locally separable linear approximation, a simple and convenient formula for DELTAE is derived and is confirmed to work well by comparison with the exact numerical calculations.