Decay rates in bistable Landau potentials driven by weakly colored Gaussian noise

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Abstract
We investigate a bistable Fokker-Planck equation describing the overdamped motion of particles in a Landau potential driven by weakly colored Gaussian noise. Our focus is on the noise-intensity dependence of the decay rates in the limit of small correlation times of the noise. In linear order of the external-noise correlation time τ the decay rates can be expressed in terms of the eigenvalues of a white-noise Fokker-Planck equation. Numerical results for the first nonvanishing eigenvalue, i.e., the inverse mean first-passage time, are presented for arbitrary noise intensity. In the limit of very low noise intensity an analytical expression is derived and in the strong-noise limit an asymptotic form is given for this eigenvalue.