  We consider Fokker-Planck type differential operators associated with general
Langevin processes admitting a Gibbs stationary distribution. Under assumptions
insuring suitable resolvent estimates, we prove Eyring-Kramers formulas for the
bottom of the spectrum of these operators in the low temperature regime. Our
approach is based on the construction of sharp Gaussian quasimodes which avoids
supersymmetry or PT-symmetry assumptions.
