SUSY Transformations for Quasinormal Modes of Open Systems
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?
Cite
@article{arxiv.math-ph/0011037,
title = {SUSY Transformations for Quasinormal Modes of Open Systems},
author = {P. T. Leung and Alec Maassen van den Brink and W. M. Suen and C. W. Wong and K. Young},
journal= {arXiv preprint arXiv:math-ph/0011037},
year = {2009}
}
Comments
14 pages, 4 figures