Hamiltonian and linear-space structure for damped oscillators: II. Critical points

2002/06/30 by S. C. Chee, S C Chee, Alec Maassen van den Brink +2 · 2 citations
Mathematics · Physics and Astronomy · #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics #math-ph #math.DS #math.MP #math.RA #physics.class-ph

paper · pdf · doi:10.1088/0305-4470/37/37/009

published as J. Phys. A _37_, 8883 (2004) · REVTeX4, 9pp., 5 PS figures. v2: extensive streamlining

arxiv created 2004/02/10 · openalex publication_date 2004/09/02 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30

Abstract

The eigenvector expansion developed in the preceding paper for a system of damped linear oscillators is extended to critical points, where eigenvectors merge and the time-evolution operator assumes a Jordan-block structure. The representation of the bilinear map is obtained in this basis. Perturbations around an M th order critical point generically lead to eigenvalue shifts ∼ 1/ M dependent on only one matrix element, with the M eigenvalues splitting in equiangular directions in the complex plane. Small denominators near criticality are shown to cancel.

Citations

• Hamiltonian and linear-space structure for damped oscillators: I. General theory

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• Hamiltonian and linear-space structure for damped oscillators: I. General theory
• Perturbation method for non-square Hamiltonians and its application to polynomial oscillators

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