Optomechanical damping basis

We present a closed-form analytical solution to the eigenvalue problem of the Liouville operator
generating the dissipative dynamics of the standard optomechanical system. The corresponding
Lindblad master equation describes the dynamics of a single-mode field inside an optical cavity
coupled by radiation pressure to its moving mirror. The optical field and the mirror are in contact
with separate environments, which are assumed at zero and finite temperature, respectively. The
optomechanical damping basis refers to the exact set of eigenvectors of the generator that, together
with the exact eigenvalues, are explicitly derived. Both the weak- and the strong-coupling regime,
which includes combined decay mechanisms, are solved in this work.

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