I'm skeptical about H&T eq. 8 to H&T eq. 9, so I'll rework as much of their math as I am capable of...
We simplify by dropping the 2 term (``In obtaining Eq. 9, we have assumed that the second term in Eq. 8 is small.''), and defining , , and , yielding
(1) |
We obtain our version of H&T eq. 9 by taking two measurements of equal mode force
0 | (2) | |
(3) | ||
(4) | ||
(5) | ||
(6) | ||
(7) |
Which is different from H&T eq. 9 by the sign in the prefactor, and the replacement .
Alternatively, noting that can vary as a function of temperature, we follow Nevo et al. in keeping it in. Using
0 | (8) | |
(9) | ||
(10) | ||
(11) | ||
(12) | ||
(13) |
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