标题： 安德森局域化或非线性波？ 概率的问题 显示英文标题

标题： Anderson localization or nonlinear waves? A matter of probability

摘要： 在线性无序系统中，安德森局域化使得任何波包在所有时间都保持局域化。 其在非线性无秩序系统中的命运正在经历激烈的理论争论和实验研究。 我们解决了这一争议，表明在任何小但有限的非线性（能量）值下，安德森局域化都有可能被破坏，并且传播的非线性波会接管。 随着非线性（能量）的增加，这种可能性也会增加，并在某个阈值处达到1，该阈值由初始波包大小决定。 此外，在固定总能量下，无限波包尺寸极限情况下，扩散概率仍然保持有限。 这些结果也推广到了更高维度。 显示英文摘要

摘要： In linear disordered systems Anderson localization makes any wave packet stay localized for all times. Its fate in nonlinear disordered systems is under intense theoretical debate and experimental study. We resolve this dispute showing that at any small but finite nonlinearity (energy) value there is a finite probability for Anderson localization to break up and propagating nonlinear waves to take over. It increases with nonlinearity (energy) and reaches unity at a certain threshold, determined by the initial wave packet size. Moreover, the spreading probability stays finite also in the limit of infinite packet size at fixed total energy. These results are generalized to higher dimensions as well.