Probing Eigenfunction Nonorthogonality by Parametric Shifts of Resonance Widths

2013/10/31 by Dmitry V. Savin, D. V. Savin, J. -B. De Vaulx +1
Chemistry · Mathematics · Physics and Astronomy · #Advanced NMR Techniques and Applications #Eigenfunction #Eigenvalues and eigenvectors #Equidistant #Geometry #Mathematics #Molecular spectroscopy and chirality #Parametric oscillator #Parametric statistics #Perturbation (astronomy) #Physics #Quantum chaos and dynamical systems #Quantum mechanics #Resonance (particle physics) #cond-mat.mes-hall #nlin.CD #nucl-th #quant-ph

paper · pdf · doi:10.12693/aphyspola.124.1074

published as Acta Phys. Pol. A 124, 1074 (2013) · 4 pages, 3 figures (references updated and typos fixed, published version)

openalex publication_date 2013/12/01 · arxiv created 2013/12/18 · arxiv updated 2013/12/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Recently, it has been shown that the change of resonance widths in an open system under a perturbation of its interior is a sensitive indicator of the nonorthogonality of resonance states. We apply this measure to quantify parametric motion of the resonances. In particular, a strong redistribution of the widths is linked with the maximal degree of nonorthogonality. Then for weakly open chaotic systems we discuss the eect of spectral rigidity on the statistical properties of the parametric width shifts, and derive the distribution of the latter in a picket-fence model with equidistant spectrum.

Citations

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• Asymmetric scattering and nonorthogonal mode patterns in optical microspirals
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• Resonance Widths in Open Microwave Cavities Studied by Harmonic Inversion
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