The state-dependence of the diffusion-controlled transport: Transitions and relaxations

The transport through a medium is primarily identified with the rate of the process and population densities inside it. The environmental conditions, such as the viscosity and temperature of the system, effectively the diffusion coefficients, govern stochastic transports. In addition, the structure of the potential characterizing the medium plays a crucial role in determining the key features of the transitions and relaxations. Here, we explore the importance of detailed information about the medium of transport in terms of the diffusion coefficient and the position of the reference point at which the rate is measured. Our study reveals that the varying positions of the states considered and the diffusion coefficient characterizing them have significant impacts on the integrated understanding of the kinetics of the diffusion-limited processes. We consider the left-to-right well transition in a double-well potential. We vary the location of the reference point systematically in the right well to measure the state-dependent rate. Interestingly, we observe that the rate exhibits a power-law relation with the distance from the barrier top. Another important perspective of our study is to consider varying diffusion coefficients for the two wells to account for the state-dependent fluctuations and explore their effects in the determination of rates of the transport processes. The observations reveal some critical aspects regarding the fundamental roles of the originating and target states in transport. The results of the current study not only enrich the elemental understanding of diffusion-controlled kinetics but also indicate the paths in developing advantageous technologies based on optimizing the conditions of transport.