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

S. C. Chee; Alec Maassen van den Brink; K. Young

doi:10.1088/0305-4470/37/37/008

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

S. C. Chee·Alec Maassen van den Brink·K. Young

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Abstract

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.

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S. C. Chee, Alec Maassen van den Brink, K. Young. 2004-02-10. Hamiltonian and Linear-Space Structure for Damped Oscillators: I. General Theory. https://doi.org/10.1088/0305-4470%2F37%2F37%2F008

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