Barrier-crossing driven by fractional Gaussian noise in the context of reactive flux formalism: An exact result

The problem of barrier-crossing is considered in the case when the surroundings of the barrier maintain some memory, while, at the same time, the heat bath is at equilibrium. The system is modelled by the generalised fractional Langevin equation with the noise term described by fractional Gaussian noise (fGn). The analytical solutions, in the time domain, are given in terms of the multinomial Mittag-Leffler function and the transmission coefficient is expressed in closed form as a function of the friction coefficient, of the barrier height, and of the Hurst exponent. Kramers’ theory rate constant is a special case of the present treatment.