On the stochastic theory of a bistable chemical reaction (Q1079881)

The stochastic kinetics of a bistable chemical reaction is studied in the birth and death formalism. An elementary perturbation technique allows to estimate the first two nontrivial eigenvalues \(\mu_ 1\) and \(\mu_ 2\) of the evolution matrix and the corresponding eigenvectors. This shows that once a quasistationary state is established in a time of order \(\tau_ 2=| \mu_ 2|^{-1}\), the final evolution only changes the probability weight of each stable state, with the relaxation time \(\tau_ 1=| \mu_ 1|^{-1}\gg \tau_ 2\) (Kramer's time). More accurate estimation of \(\mu_ 2\) and \(\mu_ 1\) is proposed and compared with exact numerical results.