A relation between massive scalar field in AdSd+1 and diffusion in channels

Abstract

It is shown that, when the diffusion coefficient is a constant and is taken a particular family of channels, the Fick-Jacobs equation is invariant under conformal symmetry. In addition, using the diffusion coefficient and the geometric parameters of the channels, a representation for the conformal algebra is obtained. Furthermore, it is found that for these systems the Fick-Jacobs equation is equivalent to the Schr¨odinger equation for the 1-dimensional conformal quantum mechanics. Moreover, using this equivalence, it is found a relation between a massive scalar field equation in AdSd+1 background and Fick-Jacobs equation, where the geometric parameter of the channels and the geometric parameters of AdSd+1 are identified