Zhang Zhenjun, Tong Peiqing, Gong Jiangbin, Li Baowen
Department of Physics, Nanjing Normal University, Nanjing, Jiangsu 210046, People's Republic of China.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 May;83(5 Pt 2):056205. doi: 10.1103/PhysRevE.83.056205. Epub 2011 May 6.
The spreading of an initially localized wave packet in one-dimensional linear and nonlinear generalized Fibonacci (GF) lattices is studied numerically. The GF lattices can be classified into two classes depending on whether or not the lattice possesses the Pisot-Vijayaraghavan property. For linear GF lattices of the first class, both the second moment and the participation number grow with time. For linear GF lattices of the second class, in the regime of a weak on-site potential, wave packet spreading is close to ballistic diffusion, whereas in the regime of a strong on-site potential, it displays stairlike growth in both the second moment and the participation number. Nonlinear GF lattices are then investigated in parallel. For the first class of nonlinear GF lattices, the second moment of the wave packet still grows with time, but the corresponding participation number does not grow simultaneously. For the second class of nonlinear GF lattices, an analogous phenomenon is observed for the weak on-site potential only. For a strong on-site potential that leads to an enhanced nonlinear self-trapping effect, neither the second moment nor the participation number grows with time. The results can be useful in guiding experiments on the expansion of noninteracting or interacting cold atoms in quasiperiodic optical lattices.
对一维线性和非线性广义斐波那契（GF）晶格中初始局域化波包的扩展进行了数值研究。根据晶格是否具有皮索特 - 维贾亚拉加万性质，GF晶格可分为两类。对于第一类线性GF晶格，二阶矩和参与数均随时间增长。对于第二类线性GF晶格，在弱在位势 regime下，波包扩展接近弹道扩散，而在强在位势 regime下，其二阶矩和参与数均呈现阶梯状增长。然后并行研究非线性GF晶格。对于第一类非线性GF晶格，波包的二阶矩仍随时间增长，但相应的参与数并非同时增长。对于第二类非线性GF晶格，仅在弱在位势下观察到类似现象。对于导致增强的非线性自陷效应的强在位势，二阶矩和参与数均不随时间增长。这些结果可用于指导准周期光学晶格中非相互作用或相互作用冷原子扩展的实验。
