Resonances as Viscosity Limits for Exponentially Decaying Potentials

Haoren Xiong

doi:10.1063/5.0016405

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arXiv · 2005.01257

Resonances as Viscosity Limits for Exponentially Decaying Potentials

Haoren Xiong

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Abstract

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 $-\Delta + V - i\epsilon x^2$, $|V(x)|\leq C e^{-2\gamma |x|}$ converge, as $ \epsilon\to 0+ $, to the poles of the meromorphic continuation of $ ( -\Delta + V -\lambda^2 )^{-1} $ uniformly on compact subsets of $\textrm{Re}\,\lambda>0$, $\textrm{Im}\,\lambda>-\gamma$, $\arg\lambda > -\pi/8$.

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Haoren Xiong. 2020-05-04. Resonances as Viscosity Limits for Exponentially Decaying Potentials. https://doi.org/10.1063/5.0016405

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