Schrödinger Equation Driven by the Square of a Gaussian Field: Instanton Analysis in the Large Amplification Limit

Philippe Mounaix

We study the tail of $p(U)$, the probability distribution of $U=|\psi (0,L){|}^2$, for $\ln U\gg 1$, $\psi (x,z)$ being the solution to $\partial_zψ-\frac{i}{2m}\nabla_{\perp}^2 ψ=g\…