Terao Takamichi
Department of Mathematical and Design Engineering, Gifu University, Gifu 501-1193, Japan.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 May;83(5 Pt 2):056611. doi: 10.1103/PhysRevE.83.056611. Epub 2011 May 31.
Localization-delocalization transition in a three-dimensional discrete nonlinear Schrödinger equation (DNLSE) with random potential is investigated, and the effect of nonlinearity is clarified numerically. By Thouless-number analysis, it is shown that the nonlinearity tends to delocalize the stationary states in a three-dimensional DNLSE. The spreading of a wave packet in a localized regime is also clarified for this system, and the subdiffusive behavior is observed in the three-dimensional system when the nonlinearity of the system is sufficiently strong. In addition, a one-dimensional DNLSE with random potential having a finite correlation length is studied, and it is suggested that the power-law exponent of the subdiffusion in DNLSE is not a universal quantity.
研究了具有随机势的三维离散非线性薛定谔方程（DNLSE）中的局域化 - 非局域化转变，并通过数值方法阐明了非线性的影响。通过 Thouless 数分析表明，非线性倾向于使三维 DNLSE 中的定态非局域化。还阐明了该系统中波包在局域区域的扩展情况，并且当系统的非线性足够强时，在三维系统中观察到亚扩散行为。此外，研究了具有有限关联长度的随机势的一维 DNLSE，并表明 DNLSE 中亚扩散的幂律指数不是一个通用量。
