dorsal/arxiv
View SchemaEigenvector Expansion and Petermann Factor for Ohmically Damped Oscillators
| Authors | Alec Maassen van den Brink, K. Young, M. H. Yung |
|---|---|
| Categories | |
| ArXiv ID | physics/0311127 |
| URL | https://arxiv.org/abs/physics/0311127 |
| DOI | 10.1088/0305-4470/39/14/015 |
| Journal | J. Phys. A: Math. Gen._39_, 3725 (2006) |
Abstract
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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"abstract": "Correlation functions $C(t) \\sim \u003c\\phi(t)\\phi(0)\u003e$ in ohmically damped\nsystems such as coupled harmonic oscillators or optical resonators can be\nexpressed as a single sum over modes $j$ (which are not power-orthogonal), with\neach term multiplied by the Petermann factor (PF) $C_j$, leading to \"excess\nnoise\" when $|C_j| \u003e 1$. It is shown that $|C_j| \u003e 1$ is common rather than\nexceptional, that $|C_j|$ can be large even for weak damping, and that the PF\nappears in other processes as well: for example, a time-independent\nperturbation $\\sim\\ep$ leads to a frequency shift $\\sim \\ep C_j$. The\ncoalescence of $J$ ($\u003e1$) eigenvectors gives rise to a critical point, which\nexhibits \"giant excess noise\" ($C_j \\to \\infty$). At critical points, the\ndivergent parts of $J$ contributions to $C(t)$ cancel, while time-independent\nperturbations lead to non-analytic shifts $\\sim \\ep^{1/J}$.",
"arxiv_id": "physics/0311127",
"authors": [
"Alec Maassen van den Brink",
"K. Young",
"M. H. Yung"
],
"categories": [
"physics.optics",
"physics.atom-ph",
"physics.class-ph"
],
"doi": "10.1088/0305-4470/39/14/015",
"journal_ref": "J. Phys. A: Math. Gen._39_, 3725 (2006)",
"title": "Eigenvector Expansion and Petermann Factor for Ohmically Damped Oscillators",
"url": "https://arxiv.org/abs/physics/0311127"
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