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arXiv · 1312.1114

Stationary solutions for multi-dimensional Gross-Pitaevskii equation with double-well potential

Andrea Sacchetti
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Abstract

In this paper we consider a non-linear Schroedinger equation with a cubic nonlinearity and a multi-dimensional double well potential. In the semiclassical limit the problem of the existence of stationary solutions simply reduces to the analysis of a finite dimensional Hamiltonian system which exhibits different behavior depending on the dimension. In particular, in dimension 1 the symmetric stationary solution shows a standard pitchfork bifurcation effect, while in dimension 2 and 3 new asymmetrical solutions associated to saddle points occur. These last solutions are localized on a single well and this fact is related to the phase transition effect observed in Bose-Einstein condensates in periodical lattices.

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Andrea Sacchetti. 2013-12-04. Stationary solutions for multi-dimensional Gross-Pitaevskii equation with double-well potential. https://doi.org/10.1088/0951-7715%2F27%2F11%2F2643

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