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

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

2002-06-18

arxiv.org/abs/math-ph/0206026v2

J. Phys. A _37_, 8865 (2004)

Physics

Mathematical Physics

REVTeX4, 10pp., 1 PS figure. N.B.: `Alec' is my first name, `Maassen van den Brink' my family name. v2: extensive streamlining

Scientific paper

10.1088/0305-4470/37/37/008

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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