Complex absorbing potential method for systems

Jimmy Kungsman; Michael Melgaard

doi:10.4064/dm469-0-1

Complex absorbing potential method for systems

Jimmy Kungsman
, Michael Melgaard

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

Abstract

The Complex Absorbing Potential (CAP) method is widely used to compute resonances in Quantum Chemistry, both for scalar valued and matrix valued Hamiltonians. In the semiclassical limit h{stroke} → 0 we consider resonances near the real axis and we establish the CAP method rigorously in an abstract matrix valued setting by proving that resonances are perturbed eigenvalues of the nonselfadjoint CAP Hamiltonian, and vice versa. The proof is based on pseudodierential operator theory and microlocal analysis.

Original language	English
Pages (from-to)	4-58
Number of pages	55
Journal	Dissertationes Mathematicae
Issue number	469
DOIs	https://doi.org/10.4064/dm469-0-1
Publication status	Published - 2010
Externally published	Yes

Keywords

Eigenvalues
Matrix valued pseudodi erential operators
Nonselfadjoint operators
Perturbations
Propagation of singularities
Scattering

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10.4064/dm469-0-1

https://arrow.tudublin.ie/scschmatart/297Licence: CC BY-NC-SA

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title = "Complex absorbing potential method for systems",

abstract = "The Complex Absorbing Potential (CAP) method is widely used to compute resonances in Quantum Chemistry, both for scalar valued and matrix valued Hamiltonians. In the semiclassical limit h\{stroke\} → 0 we consider resonances near the real axis and we establish the CAP method rigorously in an abstract matrix valued setting by proving that resonances are perturbed eigenvalues of the nonselfadjoint CAP Hamiltonian, and vice versa. The proof is based on pseudodierential operator theory and microlocal analysis.",

keywords = "Eigenvalues, Matrix valued pseudodi erential operators, Nonselfadjoint operators, Perturbations, Propagation of singularities, Scattering",

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AU - Kungsman, Jimmy

AU - Melgaard, Michael

PY - 2010

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N2 - The Complex Absorbing Potential (CAP) method is widely used to compute resonances in Quantum Chemistry, both for scalar valued and matrix valued Hamiltonians. In the semiclassical limit h{stroke} → 0 we consider resonances near the real axis and we establish the CAP method rigorously in an abstract matrix valued setting by proving that resonances are perturbed eigenvalues of the nonselfadjoint CAP Hamiltonian, and vice versa. The proof is based on pseudodierential operator theory and microlocal analysis.

AB - The Complex Absorbing Potential (CAP) method is widely used to compute resonances in Quantum Chemistry, both for scalar valued and matrix valued Hamiltonians. In the semiclassical limit h{stroke} → 0 we consider resonances near the real axis and we establish the CAP method rigorously in an abstract matrix valued setting by proving that resonances are perturbed eigenvalues of the nonselfadjoint CAP Hamiltonian, and vice versa. The proof is based on pseudodierential operator theory and microlocal analysis.

KW - Eigenvalues

KW - Matrix valued pseudodi erential operators

KW - Nonselfadjoint operators

KW - Perturbations

KW - Propagation of singularities

KW - Scattering

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DO - 10.4064/dm469-0-1

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SP - 4

EP - 58

JO - Dissertationes Mathematicae

JF - Dissertationes Mathematicae

IS - 469

ER -

Complex absorbing potential method for systems

Abstract

Keywords

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