Hamiltonian and Linear-Space Structure for Damped Oscillators: II. Critical Points

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dc.creatorChee, S. C.
dc.creatorBrink, Alec Maassen van den
dc.creatorYoung, K.
dc.date2002-06-17
dc.date2004-02-10
dc.date.accessioned2026-07-07T04:29:16Z
dc.date.available2026-07-07T04:29:16Z
dc.descriptionThe 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 $H$ assumes a Jordan-block structure. The representation of the bilinear map is obtained in this basis. Perturbations $εΔH$ around an $M$-th order critical point generically lead to eigenvalue shifts $\simε^{1/M}$ 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.
dc.descriptionREVTeX4, 9pp., 5 PS figures. v2: extensive streamlining
dc.identifierhttps://arxiv.org/abs/math-ph/0206027
dc.identifierhttp://arxiv.org/abs/math-ph/0206027
dc.identifierJ. Phys. A _37_, 8883 (2004)
dc.identifierdoi:10.1088/0305-4470/37/37/009
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/57088
dc.subjectMathematical Physics
dc.subjectDynamical Systems
dc.subjectRings and Algebras
dc.subjectClassical Physics
dc.titleHamiltonian and Linear-Space Structure for Damped Oscillators: II. Critical Points
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