Quality factor for a quantum oscillator?

I've been reading papers about nanomechanical oscillators, and the concept of quality factor often pops up. I understand to some extent about Q factor in classical sense, but since nanomechanic oscillators are often treated quantumly, what does Q factor mean then?

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There is no difference in interpretation. In both classical and quantum oscillators, if they have any dampening, the Q factor is higher the lower the dampening is. In quantum mechanics, it is common to relate the dampening to the half-life, but as far as I can tell, there is no further difference.

EDIT: the definition of Q is still the same, $\Delta f / f$ (though now that I re-read the wiki link you gave, I see that this is true only for high Q). If your system is treated quantumly, you just need to calculate the decay of the state you are interested in, or the linewidth of the energy level.

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I know the interpretation is the same, but I need a strict mathematical definition. –  C.R. Nov 27 '11 at 10:35
Because this is a physical thing, strict math definitions are without any value. deltaf/f is the definition, what else? –  Georg Nov 29 '11 at 12:31

This is just a quick answer that I'm hoping will be superseded, because I'd like to see a good answer to this question. In the context of microwave resonators etched on superconducting chips, I know from experience that the Q factor seems to be basically the $T_1$ time. Sorry I can't be more help -- this is a point of confusion for me too.

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