= Thermal representation of a reduced coupled-oscillator ground state
{title2=$\nu=\sqrt{\omega_+\omega_-}$}
Tracing one oscillator out of a symmetric coordinate-coupled Gaussian <ground state> gives a thermal density operator for an effective oscillator of <frequency> $\nu$. Its geometric ratio is $q=[(\sqrt{\omega_+}-\sqrt{\omega_-})/(\sqrt{\omega_+}+\sqrt{\omega_-})]^2$. It is generally squeezed relative to the original bare-frequency number basis. The covariance ratio fixes the effective <frequency> rather than permitting an arbitrary thermal-basis identification.
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