On the escape of the diffusing particle from the cavity

The problem of escape of a Brownian particle from a cylindrical cavity through a hole on the surface of one of the cylinder ends is considered. Using the method of surface homogenization, a one-dimensional description of the process is proposed. The solution obtained with its help allows finding the average lifetime of a particle in such a cavity with any size of the hole. Its qualitative difference from the well-known solution for the mean lifetime of a particle diffusing in an isometric (sphere-like) cavity is that the previously obtained result depends only on the volume of the cavity while the solution found in this work depends both on the volume and on the length of the cylinder.