Removal of the degeneracy in the description of electron-hole—cloud configurations

The prediction of the stable configuration of an ideal uniformly volume-pumped electron-hole cloud involves the rationalization of a "free-boundary" problem. That is to say, there are an infinite number of degenerate steady-state solutions which satisfy the fluid-dynamical equations and the boundary conditions. If the stationary states are metastable due to isolation or freedom from large-scale fluctuations in the cloud, then all states are attainable via differing initial conditions (e.g., variable risetime of the laser pump). On the other hand, if configurational changes can occur by fluctuation, creation, and annihilation of drops at any "stationary" state, however slowly, then it is necessary to specify a global thermokinetic optimum if a unique stable solution is to be identified. Both the uniquely stable and hysteresis cases are experimentally observed. In this contribution we solve the fluid-dynamical equations for a cloud, explicitly demonstrating the degenerate nature of the boundary-value problem. The global dissipation rate is evaluated and shown to be a function of the exciton-gas density as a unique internal order parameter possessing two zeros and a maximum value, and free of explicit configurational parameters. The hypothesis of a stable maximal state in a topologically fluctuating milieu (already suggested by Onsager's dissipation principle) leads near the saturation line to strictly linear global and local flux-force relations as Euler-Lagrange equations and to explicit expressions for the drop density and exciton density which are in good functional and fair quantitative accord with conventional, low-excitation stripe and cylinder pumped experiments. Our theoretical expression for the drop radius is less successful, because, we believe, of the inappropriateness of the available experimental test and the strong experimental artifacts.