隧道效应阈值以上的能流
Energy flow above the threshold of tunnel effect
摘要：
我们考虑在原点相连的两个半轴上的Klein-Gordon方程。我们在每个分支上增加一个恒定但不同的势。在以前的论文中，我们通过Hörmander版本的定相方法研究了L-无穷时间衰减。在这里，我们应用这些结果表明，对于初始条件在一个能带的隧道效应的阈值以上的一个固定部分的能量传播之间的群线。进一步我们考虑了当初始条件的能带向上移动使得粒子保持在隧道效应阈值以上时势差趋于无穷大的情况。我们表明，总的传输能量以及群线之间的部分趋于零，就像在相应的分支中的较高的潜在的平方根的倒数，如果这个潜在的趋于无穷大。同时，由群线形成的圆锥向t轴倾斜，而其孔径趋于零。
英文摘要：
We consider the Klein-Gordon equation on two half-axes connected at their origins. We add a potential that is constant but different on each branch. In a previous paper, we studied the L-infinity-time decay via Hörmander's version of the stationary phase method. Here we apply these results to show that for initial conditions in an energy band above the threshold of the tunnel effect a fixed portion of the energy propagates between group lines. Further we consider the situation that the potential difference tends to infinity while the energy band of the initial condition is shifted upwards such that the particle stays above the threshold of tunnel effect. We show that the total transmitted energy as well as the portion between the group lines tend to zero like the inverse of the square root of the higher potential in the corresponding branch if this potential tends to infinity. At the same time the cone formed by the group lines inclines to the t-axis while its aperture tends to zero.
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