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Nonlinear models and bifurcation trees in quantum mechanics: a review of recent results

  • Andrea SacchettiEmail author
Article
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Abstract

In this talk we discuss some recent results I obtained for a class of nonlinear models in quantum mechanics. In particular we focus our attention to the nonlinear one-dimensional Schrodinger equation with a periodic potential and a Stark-type perturbation. In the limit of large periodic potential the Stark–Wannier ladders of the linear equation become a dense energy spectrum because a cascade of bifurcations of stationary solutions occurs; for a detailed treatment we refer to Sacchetti (Phys Rev E 95:062212, 2017, SIAM J Math Anal 50(6):5783–5810, 2018) where this model has been studied.

Keywords

Gross–Pitaevskii equation Bose–Einstein condensates Bifurcation tree 

Mathematics Subject Classification

35Q55 81Qxx 81T25 

Notes

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Copyright information

© Università degli Studi di Napoli "Federico II" 2019

Authors and Affiliations

  1. 1.Department of Physics, Informatics and MathematicsUniversity of Modena e Reggio EmiliaModenaItaly

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