Eigenvector Expansion and Petermann Factor for Ohmically Damped Oscillators

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dc.creatorBrink, Alec Maassen van den
dc.creatorYoung, K.
dc.creatorYung, M. H.
dc.date2003-11-26
dc.date2006-03-24
dc.date.accessioned2026-07-07T06:36:21Z
dc.date.available2026-07-07T06:36:21Z
dc.descriptionCorrelation functions $C(t) \sim <ϕ(t)ϕ(0)>$ 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 $\sim \ep^{1/J}$.
dc.descriptionREVTeX4, 14 pages, 4 figures. v2: final, 20 single-col. pages, 2 figures. Streamlined with emphasis on physics over formalism; rewrote Section V E so that it refers to time-dependent (instead of non-equilibrium) effects
dc.identifierhttps://arxiv.org/abs/physics/0311127
dc.identifierhttp://arxiv.org/abs/physics/0311127
dc.identifierJ. Phys. A: Math. Gen._39_, 3725 (2006)
dc.identifierdoi:10.1088/0305-4470/39/14/015
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/100054
dc.subjectOptics
dc.subjectAtomic Physics
dc.subjectClassical Physics
dc.titleEigenvector Expansion and Petermann Factor for Ohmically Damped Oscillators
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