Resonances as viscosity limits for exponentially decaying potentials

Haoren Xiong

doi:10.1063/5.0016405

Resonances as viscosity limits for exponentially decaying potentials

Haoren Xiong^*

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We show that the complex absorbing potential method for computing scattering resonances applies to the case of exponentially decaying potentials. This means that the eigenvalues of -Δ + V - iϵx² and |V(x)| ≤ Ce^-2γ|x|converge, as ϵ → 0+, to the poles of the meromorphic continuation of (-Δ + V - λ²)^-1uniformly on compact subsets of Re λ > 0, Im λ > - γ, and arg λ > -π/8.

Original language	English
Article number	022101
Number of pages	13
Journal	Journal of Mathematical Physics
Volume	62
Issue number	2
DOIs	https://doi.org/10.1063/5.0016405
Publication status	Published - 19 Feb 2021

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1063/5.0016405

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title = "Resonances as viscosity limits for exponentially decaying potentials",

abstract = "We show that the complex absorbing potential method for computing scattering resonances applies to the case of exponentially decaying potentials. This means that the eigenvalues of -Δ + V - iϵx2 and |V(x)| ≤ Ce-2γ|x| converge, as ϵ → 0+, to the poles of the meromorphic continuation of (-Δ + V - λ2)-1 uniformly on compact subsets of Re λ > 0, Im λ > - γ, and arg λ > -π/8.",

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AU - Xiong, Haoren

PY - 2021/2/19

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N2 - We show that the complex absorbing potential method for computing scattering resonances applies to the case of exponentially decaying potentials. This means that the eigenvalues of -Δ + V - iϵx2 and |V(x)| ≤ Ce-2γ|x| converge, as ϵ → 0+, to the poles of the meromorphic continuation of (-Δ + V - λ2)-1 uniformly on compact subsets of Re λ > 0, Im λ > - γ, and arg λ > -π/8.

AB - We show that the complex absorbing potential method for computing scattering resonances applies to the case of exponentially decaying potentials. This means that the eigenvalues of -Δ + V - iϵx2 and |V(x)| ≤ Ce-2γ|x| converge, as ϵ → 0+, to the poles of the meromorphic continuation of (-Δ + V - λ2)-1 uniformly on compact subsets of Re λ > 0, Im λ > - γ, and arg λ > -π/8.

UR - https://www.scopus.com/pages/publications/85101380169

U2 - 10.1063/5.0016405

DO - 10.1063/5.0016405

M3 - Article

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SN - 0022-2488

VL - 62

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

IS - 2

M1 - 022101

ER -

Resonances as viscosity limits for exponentially decaying potentials

Abstract

ASJC Scopus subject areas

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