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SUSY Transformations for Quasinormal and Total-Transmission 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

Quasinormal modes are the counterparts in open systems of normal modes in conservative systems; defined by outgoing-wave boundary conditions, they have complex eigenvalues. The conditions are studied for a system to have a supersymmetric(SUSY) partner with the same complex quasinormal-mode spectrum (or the same except for one eigenvalue). The discussion naturally includes total-transmission modes as well(incoming at one extreme and outgoing at the other). Several types of SUSY transformations emerge, and each is illustrated with examples, including the transformation among different Poschl-Teller potentials and the well-known identity in spectrum between the two parity sectors of linearized gravitational waves propagating on a Schwarzschild background. In contrast to the case of normal modes, there may be multiple essentially isospectral partners, each missing a different state. The SUSY transformation preserves orthonormality under a bilinear map which is the analog of the usual inner product for conservative systems. SUSY transformations can lead to doubled quasinormal and total-transmission modes; this phenomenon is analysed and illustrated. The existence or otherwise of SUSY partners is also relevant to the question of inversion: are open wave systems uniquely determined by their complex spectra?

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P. T. Leung, Alec Maassen van den Brink, W. M. Suen, C. W. Wong, K. Young. 1999-09-28. SUSY Transformations for Quasinormal and Total-Transmission Modes of Open Systems. https://arxiv.org/abs/math-ph/9909030

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