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SUSY Transformations for Quasinormal Modes of Open Systems

P. T. Leung·Alec Maassen van den Brink·W. M. Suen·C. W. Wong·K. Young
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Abstract

Supersymmetry (SUSY) in quantum mechanics is extended from square-integrable states to those satisfying the outgoing-wave boundary condition, in a Klein-Gordon formulation. This boundary condition allows both the usual normal modes and quasinormal modes with complex eigenvalues. The simple generalization leads to three features: the counting of eigenstates under SUSY becomes more systematic; the linear-space structure of outgoing waves (nontrivially different from the usual Hilbert space of square-integrable states) is preserved by SUSY; and multiple states at the same frequency (not allowed for normal modes) are also preserved. The existence or otherwise of SUSY partners is furthermore relevant to the question of inversion: are open systems uniquely determined by their complex outgoing-wave spectra?

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BibTeXRIS

P. T. Leung, Alec Maassen van den Brink, W. M. Suen, C. W. Wong, K. Young. 2000-11-23. SUSY Transformations for Quasinormal Modes of Open Systems. https://doi.org/10.1063/1.1388900

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