Classical relaxation in a double well

The canonical ensemble position and velocity autocorrelation functions (X and V ACF's) and the power spectra are obtained for a classical particle at T ≈ Γ, Γ ≡barrier height in a symmetric double-well (DW) potential. We report the presence of well defined temperature dependent characteristics frequencies in the VACF and the XACF, both above and below the harmonic frequency in this strongly anharmonic regime. A striking feature of the DW relaxation is that the V (X)ACF's are weakly temperature dependent at T ≈ Γ.