Spatiotemporal properties of diffusive systems with a mobile imperfect trap

We study analytically a one-dimensional system initially uniformly filled with diffusing particles [Formula Presented], and a single imperfect mobile trap [Formula Presented] initially located at the origin, [Formula Presented]. For arbitrary values of diffusion constants [Formula Presented] [Formula Presented] and any trapping rate constant [Formula Presented], we calculate exactly the total rate of trapping as well as the asymptotic concentration of [Formula Presented]’s at [Formula Presented]. For [Formula Presented] we also analytically derive the local rate of trapping and the concentration of [Formula Presented]’s at any point [Formula Presented]. Characteristic length scales and extensions to higher dimensions are also discussed.