Resolving the Free Boundary Problem for Electron-Hole Drops

Abstract

<p>The prediction of the stable configuration of a cloud of electron-hole drops involves the resolution of a "free boundary" problem. That is to say, the constraint of steady state relationships is not enough to uniquely determine a stable steady state. There are an infinite number of states which satisfy the boundary conditions. If these stationary states are metastable due to isolation or freedom from large scale fluctuations then different system histories will produce different observable states and hysteresis phenomena. However, if configurational changes can occur through fluctuations, either by creation or annihilation of drops, however slowly, it is necessary to specify an optimizing process to identify a unique stable solution.</p> <p>In this thesis a simple model is used to describe the cloud, explicitly demonstrating the "free boundary" problem. The optimizing function is taken to the rate of entropy production, the optimum being a maximum in the dissipation. The optimization process leads to linear global and local flux-force relationships and to explicit expressions for drop density and exciton gas density which are in good functional and quantitative accord with experiments.</p>