Quantum-Statistical Metastability

Consider a system rendered unstable by both quantum tunneling and thermodynamic fluctuation. The tunneling rate $\Gamma$, at temperature ${\beta }^{-1\mathrm{}}$, is related to the free energy $F$ by $\Gamma =\left(\frac{2}{\hslash }\right)\mathrm{Im}F$. However, the classical escape rate is $\Gamma =\left(\frac{\omega \beta }{\pi }\right)\mathrm{Im}F$, $-{\omega }^2$ being the negative eigenvalue at the saddle point. A general theory of metastability is constructed in which these formulas are true for temperatures, respectively, below and above $\frac{\omega \hslash }{2\pi }$ with a narrow transition region of $O\left({\hslash }^{\frac{3}{2}}\right)$.