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- W4381856635 abstract "We study the tail of $p(U)$, the probability distribution of $U=vertpsi(0,L)vert^2$, for $ln Ugg 1$, $psi(x,z)$ being the solution to $partial_zpsi -frac{i}{2m}nabla_{perp}^2 psi =gvert Svert^2, psi$, where $S(x,z)$ is a complex Gaussian random field, $z$ and $x$ respectively are the axial and transverse coordinates, with $0le zle L$, and both $mne 0$ and $g>0$ are real parameters. We perform the first instanton analysis of the corresponding Martin-Siggia-Rose action, from which it is found that the realizations of $S$ concentrate onto long filamentary instantons, as $ln Uto +infty$. The tail of $p(U)$ is deduced from the statistics of the instantons. The value of $g$ above which $langle Urangle$ diverges coincides with the one obtained by the completely different approach developed in Mounaix et al. 2006 {it Commun. Math. Phys.} {bf 264}~741. Numerical simulations clearly show a statistical bias of $S$ towards the instanton for the largest sampled values of $ln U$. The high maxima -- or `hot spots' -- of $vert S(x,z)vert^2$ for the biased realizations of $S$ tend to cluster in the instanton region." @default.
- W4381856635 created "2023-06-25" @default.
- W4381856635 creator A5078246196 @default.
- W4381856635 date "2023-07-11" @default.
- W4381856635 modified "2023-10-06" @default.
- W4381856635 title "Schrödinger equation driven by the square of a Gaussian field: instanton analysis in the large amplification limit" @default.
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- W4381856635 doi "https://doi.org/10.1088/1751-8121/ace0e8" @default.
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