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I'm studying dynamics of a quantum network of coupled oscillators driven by an external force. Am I doing right, if I calculate signal-to-noise ratio by dividing the expectation value of oscillator position to standard deviation of it?

To expectation value be in hand, I'm using solution of coupled differential equations compacted in this form $$\frac{du}{dt} = Au(t) + n(t)$$ obtained by Langevin equations. For the standard deviation also, I'm using covariance matrix of the system.

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