Soft trapping lasts longer: Dwell time of a Brownian particle varied by potential shape

It is often regarded that the dwell time (or residence time, escape time, trapping duration) of trapped Brownian particles is described by the multiplication of two separate factors, i.e., the diffusive traveling time of the trapping domain size without taking into account the trapping force, and the stochastic event of overcoming the trapping energy by thermal one instantaneously. However, we show that the ratio of dwell time to the typical traveling time for the trapping domain size depends on the shape of the force field. The shape of the trapping potential affects this ratio even if the trapping energy gap is the same and the smooth potential has a single minimum. Our finding suggests the possible application of the potential shape to realize the desired trapping characteristics.