Abstract:We study the tail of $p(U)$, the probability distribution of $U=\vert\psi(0,L)\vert^2$, for $\ln U\gg 1$, $\psi(x,z)$ being the solution to $\partial_z\psi -\frac{i}{2m}\nabla_{\perp}^2 \psi =g\vert S\vert^2\, \psi$, where $S(x,z)$ is a complex Gaussian random field, $z$ and $x$ respectively are the axial and transverse coordinates, with $0\le z\le L$, and both $m\ne 0$ and $g>0$ are real parameters. We perform the first instanton analysis of the corresponding Martin-Siggia-Rose action, from which it is fou… Show more
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