非线性Schreodinger方程中Stationary States的局部化长度
The Localization Length of Stationary States in the Nonlinear Schreodinger Equation
摘要：
对于非线性Schreodinger方程（NLSE），在存在无序的情况下，我们发现了指数定域定态，在本文中，我们用解析方法证明了定域长度与非线性的强度无关，并且与相应线性方程的定域长度相同。分析利用固定NLSE和朗之万方程以及由此产生的福克-普朗克方程之间的对应关系。对“白噪声”随机势进行了计算，并解析地得到了本征态指数增长的精确表达式。有人认为，主要结论是强大的。
英文摘要：
For the nonlinear Schreodinger equation (NLSE), in presence of disorder, exponentially localized stationary states are found. In the present Letter it is demonstrated analytically that the localization length is typically independent of the strength of the nonlinearity and is identical to the one found for the corresponding linear equation. The analysis makes use of the correspondence between the stationary NLSE and the Langevin equation as well as of the resulting Fokker-Planck equation. The calculations are performed for the ``white noise'' random potential and an exact expression for the exponential growth of the eigenstates is obtained analytically. It is argued that the main conclusions are robust.
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