Multifractals Competing with Solitons on Fibonacci Optical Lattice

Details Multifractals Competing with Solitons on Fibonacci Optical Lattice Multifractals Competing with Solitons on Fibonacci Optical Lattice

2011-10-27

arxiv.org/abs/1110.6328v2

Physics

Condensed Matter

Quantum Gases

5 pages, 4 figures

Scientific paper

We study the stationary states for the nonlinear Schr\"odinger equation on the Fibonacci lattice which is expected to be realized by Bose-Einstein condensates loaded into an optical lattice. When the model does not have a nonlinear term, the wavefunctions and the spectrum are known to show fractal structures. Such wavefunctions are called critical. We present a phase diagram of the energy spectrum for varying the nonlinearity. It consists of three portions, a forbidden region, the spectrum of critical states, and the spectrum of stationary solitons. We show that the energy spectrum of critical states remains intact irrespective of the nonlinearity in the sea of a large number of stationary solitons.

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