隧道效应对L-无限时间衰变的影响
The Influence of the Tunnel Effect on L-infinity-time decay
摘要：
我们考虑由n个半轴在原点连接而成的星形网络上的Klein-Gordon方程。我们加上一个势，它是常数，但在每个分支上不同。利用谱理论的解决方案公式从以前的文件，我们研究了L-无穷时间衰减通过Hörmander的版本的固定相方法。我们分析了解关于时间的渐近展开的首项ct ^{-1/2}的系数c。对于两个分支，我们证明，对于一个初始条件在一个能带以上的隧道效应的阈值，这个系数趋于零的分支具有较高的潜力，作为潜在的差异趋于无穷大。同时，t^{-1/2}衰变在（t，x）平面上的锥孔和对t轴的倾斜度趋于零。
英文摘要：
We consider the Klein-Gordon equation on a star-shaped network composed of n half-axes connected at their origins. We add a potential which is constant but different on each branch. Exploiting a spectral theoretic solution formula from a previous paper, we study the L-infinity-time decay via Hörmander's version of the stationary phase method. We analyze the coefficient c of the leading term c t^{-1/2} of the asymptotic expansion of the solution with respect to time. For two branches we prove that for an initial condition in an energy band above the threshold of tunnel effect, this coefficient tends to zero on the branch with the higher potential, as the potential difference tends to infinity. At the same time the incline to the t-axis and the aperture of the cone of t^{-1/2}-decay in the (t,x)-plane tend to zero.
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