Propagation Effects on the Breakdown of a Linear Amplifier Model: Complex-Mass Schrodinger Equation Driven by the Square of a Gaussian Field

Philippe Mounaix, Pierre Collet, Joel L. Lebowitz

Solutions to the equation ${\partial }_t\mathcal{E}(x,t)-\frac{i}{2m}\Delta \mathcal{E}(x,t)=\lambda |S(x,t){|}^2\mathcal{E}(x,t)$ are investigated, where $S(x,t)$ is a complex Gaussian field with zero mean…