论文标题
牛顿多边形和多个三角洲的共振
Newton polygons and resonances of multiple delta-potentials
论文作者
论文摘要
我们证明了在$ \ Mathbb {r} $上的$ H $依赖性delta-function电位的设置中的半经典散射共振位置的明确渐近学。在两个或三个三角极点的情况下，我们能够证明与$ \ im z \ im z \ sim-γH\ log（1/h）的特定行发生共振。$更一般地，我们使用牛顿多边形的方法来表明，真实轴附近的共振可能只会出现此类有限的收集，我们可能会出现更多的迹象，我们可能会出现更多的证明$ num of Paramse $ $ numer $ $ unde $ unde $。大量的三角极点的值$γ$。
We prove explicit asymptotics for the location of semiclassical scattering resonances in the setting of $h$-dependent delta-function potentials on $\mathbb{R}$. In the cases of two or three delta poles, we are able to show that resonances occur along specific lines of the form $\Im z \sim -γh \log(1/h).$ More generally, we use the method of Newton polygons to show that resonances near the real axis may only occur along a finite collection of such lines, and we bound the possible number of values of the parameter $γ.$ We present numerical evidence of the existence of more and more possible values of $γ$ for larger numbers of delta poles.
