离散非线性薛定谔方程的实验结果
Experimental Results Related to Discrete Nonlinear Schrödinger Equations
摘要：
在本章中，我们讨论实现离散非线性薛定谔（DNLS）方程的实验。这种描述的相关性来自于三个共同特征的竞争：非线性、分散性和空间中的中到大水平（周期、准周期或随机）离散性。DNLS方程在原子和分子物理学中特别普遍，用于研究光晶格或超晶格中的玻色-爱因斯坦凝聚体;在非线性光学中用于描述波导阵列和光折变晶体中的脉冲传播。非线性光学和玻色-爱因斯坦凝聚的新实验为DNLS模型提供了新的挑战，DNLS和相关方程最近也被用于在新的物理环境中进行重要的预测，例如复合超材料和超导器件阵列的研究。
英文摘要：
In this chapter, we discuss experiments that realize the discrete nonlinear Schrödinger (DNLS) equations. The relevance of such descriptions arises from the competition of three common features: nonlinearity, dispersion, and a medium to large level of (periodic, quasiperiodic, or random) discreteness in space. DNLS equations have been especially prevalent in atomic and molecular physics in the study of Bose-Einstein condensates in optical lattices or superlattices; and in nonlinear optics in the description of pulse propagation in waveguide arrays and photorefractive crystals. New experiments in both nonlinear optics and Bose-Einstein condensation provide new challenges for DNLS models, and DNLS and related equations have also recently been used to make important predictions in novel physical settings such as the study of composite metamaterials and arrays of superconducting devices.
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