论文标题
共鸣是指数衰减电位的粘度限制
Resonances as Viscosity Limits for Exponentially Decaying Potentials
论文作者
论文摘要
我们表明，用于计算散射共振的复杂吸收电位（CAP）方法适用于指数衰减的电位。这意味着$-Δ+ v -iεx^2 $，$ | v（x）| \ leq c e^{ - 2γ| x |} $的特征值commenge，as $ε\ to 0+ $，to $（ - δ+ v -λ^2）^{ - + v -λ^2） $ \ textrm {re} \，λ> 0 $，$ \ textrm {im} \，λ>-γ$，$ \argλ>-π/8 $。
We show that the complex absorbing potential (CAP) method for computing scattering resonances applies to the case of exponentially decaying potentials. That means that the eigenvalues of $-Δ+ V - iεx^2$, $|V(x)|\leq C e^{-2γ|x|}$ converge, as $ ε\to 0+ $, to the poles of the meromorphic continuation of $ ( -Δ+ V -λ^2 )^{-1} $ uniformly on compact subsets of $\textrm{Re}\,λ>0$, $\textrm{Im}\,λ>-γ$, $\argλ> -π/8$.
