%0 Generic %1 takahashi2011multifractals %A Takahashi, M. %A Katsura, H. %A Kohmoto, M. %A Koma, T. %D 2011 %K fractals %T Multifractals Competing with Solitons on Fibonacci Optical Lattice %U http://arxiv.org/abs/1110.6328 %X We study the stationary states for the nonlinear Schrödinger 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.

@misc{takahashi2011multifractals, abstract = {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.}, added-at = {2012-08-10T00:02:41.000+0200}, author = {Takahashi, M. and Katsura, H. and Kohmoto, M. and Koma, T.}, biburl = {https://www.bibsonomy.org/bibtex/240a79d1a7e5b339290fde319e70aad36/vakaryuk}, description = {Multifractals Competing with Solitons on Fibonacci Optical Lattice}, interhash = {be1ff78c06f3b05d4e852bdfaa3ebacb}, intrahash = {40a79d1a7e5b339290fde319e70aad36}, keywords = {fractals}, note = {cite arxiv:1110.6328 Comment: 5 pages, 4 figures, major revision, references added}, timestamp = {2012-08-10T00:02:41.000+0200}, title = {Multifractals Competing with Solitons on Fibonacci Optical Lattice}, url = {http://arxiv.org/abs/1110.6328}, year = 2011 }