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- W4323865327 abstract "We devise an analytical method to deal with a class of nonlinear Schrödinger lattices with random potential and subquadratic power nonlinearity. An iteration algorithm is proposed based on the multinomial theorem, using Diophantine equations and a mapping procedure onto a Cayley graph. Based on this algorithm, we are able to obtain several hard results pertaining to asymptotic spreading of the nonlinear field beyond a perturbation theory approach. In particular, we show that the spreading process is subdiffusive and has complex microscopic organization involving both long-time trapping phenomena on finite clusters and long-distance jumps along the lattice consistent with Lévy flights. The origin of the flights is associated with the occurrence of degenerate states in the system; the latter are found to be a characteristic of the subquadratic model. The limit of quadratic power nonlinearity is also discussed and shown to result in a delocalization border, above which the field can spread to long distances on a stochastic process and below which it is Anderson localized similarly to a linear field." @default.
- W4323865327 created "2023-03-11" @default.
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- W4323865327 date "2023-03-10" @default.
- W4323865327 modified "2023-09-23" @default.
- W4323865327 title "Dynamical chaos in nonlinear Schrödinger models with subquadratic power nonlinearity" @default.
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- W4323865327 doi "https://doi.org/10.1103/physreve.107.034203" @default.
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