arXiv subjects

S. C. Chee

Publications and source records attributed to S. C. Chee.

2 recordsLinked to original sources

arXiv2004

Hamiltonian and Linear-Space Structure for Damped Oscillators: I. General Theory

The phase space of $N$ damped linear oscillators is endowed with a bilinear map under which the evolution operator is symmetric. This analog of self-adjointness allows properties familiar from conservative systems to be recovered, e.g., eigenvectors are "orthogonal" under the bilinear map and obey sum rules, initial-value problems are readily solved and perturbation theory applies to the_complex_ eigenvalues. These concepts are conveniently represented in a biorthogonal basis.

math-ph↗

arXiv2004

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

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 $H$ 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.

math-ph↗