Eigenvector Expansion and Petermann Factor for Ohmically Damped Oscillators

Details Eigenvector Expansion and Petermann Factor for Ohmically Damped Oscillators Eigenvector Expansion and Petermann Factor for Ohmically Damped Oscillators

2003-11-26

arxiv.org/abs/physics/0311127v2

J. Phys. A: Math. Gen._39_, 3725 (2006)

Physics

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REVTeX4, 14 pages, 4 figures. v2: final, 20 single-col. pages, 2 figures. Streamlined with emphasis on physics over formalism;

Scientific paper

10.1088/0305-4470/39/14/015

Correlation functions $C(t) \sim <\phi(t)\phi(0)>$ in ohmically damped systems such as coupled harmonic oscillators or optical resonators can be expressed as a single sum over modes $j$ (which are not power-orthogonal), with each term multiplied by the Petermann factor (PF) $C_j$, leading to "excess noise" when $|C_j| > 1$. It is shown that $|C_j| > 1$ is common rather than exceptional, that $|C_j|$ can be large even for weak damping, and that the PF appears in other processes as well: for example, a time-independent perturbation $\sim\ep$ leads to a frequency shift $\sim \ep C_j$. The coalescence of $J$ ($>1$) eigenvectors gives rise to a critical point, which exhibits "giant excess noise" ($C_j \to \infty$). At critical points, the divergent parts of $J$ contributions to $C(t)$ cancel, while time-independent perturbations lead to non-analytic shifts $\sim \ep^{1/J}$.

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