Diffusion in a fluid flow generated by a source at the apex of a wedge

Abstract

We consider a particle diffusing inside a wedge with absorbing boundaries and driven by a radial flow of incompressible fluid generated by a source at the apex. The survival probability decays as (time)^{-b} with exponent depending on the opening angle of the wedge and the Reynolds number associated with the hydrodynamic flow. The computation of the decay exponent reduces to finding the ground state energy of the quantum particle in an infinitely deep potential well with shape determined by the radial flow velocity.