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arXiv 1210.0002physics.opticscond-mat.dis-nn
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安德森局域化的孤子化

Solitonization of the Anderson Localization

Claudio Conti

摘要:

研究了在高斯随机势存在下一维非线性薛定谔方程的亮孤子形状与无序诱导局域化的形状之间的关系。重点讨论了具有随机势的非线性Schroedinger方程的束缚态的聚焦非线性,对于局域化程度最高的束缚态,利用微扰理论和变分方法,按照无序系统的统计力学方法,得到了非线性本征值和局域化长度的显式表达式.我们数值研究的线性稳定性和“超局域化”。发现无序平均安德森局域化的分布服从非局域非线性薛定谔方程

英文摘要:

We study the affinities between the shape of the bright soliton of the one-dimensional nonlinear Schroedinger equation and that of the disorder induced localization in the presence of a Gaussian random potential. With emphasis on the focusing nonlinearity, we consider the bound states of the nonlinear Schroedinger equation with a random potential; for the state exhibiting the highest degree of localization, we derive explicit expressions for the nonlinear eigenvalue and for the localization length by using perturbation theory and a variational approach following the methods of statistical mechanics of disordered systems. We numerically investigate the linear stability and "superlocalizations". The profile of the disorder averaged Anderson localization is found to obey a nonlocal nonlinear Schroedinger equation

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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