Abstract
The quasistationary decay rate of a metastable state, RD, often is interpreted as the inverse of the average lifetime of this state, τa. There are two ways for finding the rate: to evaluate it using one of the approximate Kramers formulas or to extract the rate RD from numerical modeling. We study quantitatively to what extent the inverse decay rate can be identified with the mean lifetime and to what extent the approximate and numerical quasistationary rates agree with each other. This is done for the values of dissipation strength covering 4 orders of magnitude. Both the numerical rate and the average lifetime are obtained from computer modeling of the decay process using the stochastic differential equations for the phase space diffusion. It is shown that at lower temperature, the numerical rate is in agreement with the inverse lifetime whereas at weak friction and high temperature, τa exceeds \( {R}_D^{-1} \) by up to 50%. The Kramers formula for the decay rate at strong friction is found to be in a good agreement with the dynamical rate deviating typically by 5%. For weak friction, the agreement is substantially worse: the difference varies from 20% to a factor of 2.
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Chushnyakova, M.V., Gontchar, I.I. Precision Numerical Modeling of the Decay of a Metastable State at High Temperatures. Braz J Phys 49, 587–593 (2019). https://doi.org/10.1007/s13538-019-00671-8
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DOI: https://doi.org/10.1007/s13538-019-00671-8