Physics – Condensed Matter – Quantum Gases
Scientific paper
2011-10-14
J. Math. Phys. 52, 092701 (2011)
Physics
Condensed Matter
Quantum Gases
17 pages, 9 figures
Scientific paper
We study a discrete nonlinear Schr\"odinger lattice with a parabolic trapping potential. The model, describing, e.g., an array of repulsive Bose-Einstein condensate droplets confined in the wells of an optical lattice, is analytically and numerically investigated. Starting from the linear limit of the problem, we use global bifurcation theory to rigorously prove that - in the discrete regime - all linear states lead to nonlinear generalizations thereof, which assume the form of a chain of discrete dark solitons (as the density increases). The stability of the ensuing nonlinear states is studied and it is found that the ground state is stable, while the excited states feature a chain of stability/instability bands. We illustrate the mechanisms under which discreteness destabilizes the dark-soliton configurations, which become stable only inside the continuum regime. Continuation from the anti-continuum limit is also considered, and a rich bifurcation structure is revealed.
Achilleos V.
Diakonos Fotios K.
Frantzeskakis Dimitri J.
Karachalios Nikos I.
Kevrekidis Panagiotis G.
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