Plancks Other Quanta: Corpuscular Electrodiffusion

When B"acklund transformations are applied repeatedly to any solution of the nonlinear equations describing electrodiffusion through a liquid junction separating two infinite well-stirred layers, they give rise to quantized ionic fluxes across the junction. A particular exact solution is shown to imply that these fluxes consist of quanta of electric charge.

💡 Research Summary

The paper investigates the nonlinear electrodiffusion equations that describe ion transport through a liquid junction separating two infinitely large, well‑stirred electrolyte layers. Starting from the classical Nernst‑Planck‑Poisson (NPP) system, the author introduces a Bäcklund transformation—a tool originally developed in the theory of integrable nonlinear equations—to generate new solutions from any given solution of the NPP system. By applying the transformation repeatedly, a hierarchy of solutions is constructed in which each iteration adds a fixed increment to the ionic concentrations, the electric field, and consequently the ionic current density.

Mathematically, if ((c_{+}^{(0)},c_{-}^{(0)},E^{(0)})) denotes an arbitrary seed solution, the (n)-th Bäcklund‑generated solution takes the form
\