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Ba Phi Nguyen,Quang Minh Ngo,Kihong Kim 한국물리학회 2016 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.68 No.3
We consider the spreading of an initially localized wave packet in one-dimensional hybrid orderedquasiperiodic lattices. We consider two diffrent kinds of quasiperiodic sequences, which are the Cantor and the period-doubling sequences. From numerical calculations based on the discrete Schr¨odinger equation, we demonstrate that hybrid ordered-quasiperiodic lattices can support the super-ballistic spreading of a wave packet with very large spreading exponents for certain transient time windows. Remarkably, in the case of the sublattice with the on-site potential obeying the period-doubling quasiperiodic sequence, we find that the super-ballistic exponent can be larger than six. We also point out that previous explanations of this phenomenon based on a generalized version of the point source model are incorrect.
Ba Phi Nguyen,김기홍 한국물리학회 2014 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.64 No.3
We study numerically the dynamics of an initially localized wave packet in one-dimensional nonlinearSchr¨odinger lattices with both local and nonlocal nonlinearities. Using the discrete nonlinearSchr¨odinger equation generalized by including a nonlocal nonlinear term, we calculate four differentphysical quantities as a function of time, which are the return probability to the initial excitationsite, the participation number, the root-mean-square displacement from the excitation site and thespatial probability distribution. We investigate the influence of the nonlocal nonlinearity on thedelocalization to self-trapping transition induced by the local nonlinearity. In the non-self-trappingregion, we find that the nonlocal nonlinearity compresses the soliton width and slows down thespreading of the wave packet. In the vicinity of the delocalization to self-trapping transition pointand inside the self-trapping region, we find that a new kind of self-trapping phenomenon, which wecall partial self-trapping, takes place when the nonlocal nonlinearity is sufficiently strong.