Distribution of interacting ionic particles in disordered media

The equilibrium distribution of ionic particles in a charged disordered background is studied using the nonlinear Poisson-Boltzmann equation. For interacting ions in an arbitrarily given realization of the disorder, an exact solution of the equation is obtained in one dimension using a mapping of the nonlinear Poisson-Boltzmann equation to a self-consistent Schrödinger equation. It is shown that the ions are not distributed so as to locally neutralize the background, presumably due to their mutual interactions.