Reversible escape from a well across a barrier by diffusion in one dimension

Abstract

Escape by diffusion in one dimension from a parabolic well across a parabolic barrier is investigated for a range of barrier heights. The probability of occupation of the well decays at long times inversely with the square root of time due to repeated return to the well after excursion in the outer space. The amplitude of the long-time tail increases as the barrier gets lower. The time dependence of the occupation probability can be described by a phenomenological rate equation with memory term and with a source term describing the rate of return from the outer space. For moderately high barrier the rate coefficient deviates from the Kramers expression.