论文标题
散射阶段：终于看到
The scattering phase: seen at last
论文作者
论文摘要
散射阶段定义为$ \ log \ det s（λ） /2πi$，其中$ s（λ）$是（单一的）散射矩阵，是与外部域的计数函数的类似物，并且与外部域交易，并且与Kerin的频谱移位功能密切相关。我们对散射阶段的渐近学进行了经典结果，并指出在强烈捕获波的情况下，它绝不是单调的。也许更重要的是，我们提供了非主要散射器的散射阶段的第一个数值计算。他们表明，即使在低频率下，渐近的Weyl定律也是准确的，并且揭示了诱捕的影响，例如缺乏单调性。这是通过使用最近的高级多物理有限元软件FreeFem来实现的。
The scattering phase, defined as $ \log \det S ( λ) / 2πi $ where $ S ( λ) $ is the (unitary) scattering matrix, is the analogue of the counting function for eigenvalues when dealing with exterior domains and is closely related to Krein's spectral shift function. We revisit classical results on asymptotics of the scattering phase and point out that it is never monotone in the case of strong trapping of waves. Perhaps more importantly, we provide the first numerical calculations of scattering phases for non-radial scatterers. They show that the asymptotic Weyl law is accurate even at low frequencies and reveal effects of trapping such as lack of monotonicity. This is achieved by using the recent high level multiphysics finite element software FreeFEM.
