Haus/Gross-Pitaevskii equation for random lasers

We report on experimental tests of the trend of random laserlinewidth versus pumping power as predicted by an Haus master equation that is formally identical to the one-dimensional Gross- Pitaevskii equation in an harmonic potential. Experiments are done by employing picosecond pumped dispersions of Titaniumdioxide particles in dye-doped methanol. The derivation of the master equations is also detailed and shown to be in agreement with experiments analytically predicting the value of the threshold linewidth.