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Insight toward the first-passage time in a bistable potential with highly colored noise
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The exponential coefficient in the first-passage-time problem for a bistable potential with highly colored noise is predicted to be (8/27 by all existing theories. On the other hand, we show herein that all existing numerical evidence seems to indicate that the coefficient is actually larger by about (4/3, i.e., that the numerical factor in the exponent is approximately (32/81. Existing data cover values of ¿V0/D up to ~20, where V0 is the barrier height, ¿ the correlation time of the noise, and D the noise intensity. We provide an explanation for the modified coefficinet, the explanation also being based on existing numerical simulations. Whether the value (8/27 predicted by all large-¿ theories is achieved for even larger values of ¿V0/D is unknown but appears questionable (except perhaps for enormously large, experimentally inaccessible values of this factor) in view of currently available results.
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LINDENBERG, Katja, et al. Insight toward the first-passage time in a bistable potential with highly colored noise. Physical Review A. 1989. Vol. 40, num. 7, pags. 4157-4160. ISSN 1050-2947. [consulted: 3 of August of 2026]. Available at: https://hdl.handle.net/2445/9462