一维非线性薛定谔方程晶格模型在热噪声背景下的能量输运

项目名称： 一维非线性薛定谔方程晶格模型在热噪声背景下的能量输运

项目编号： No.11205114

项目类型： 青年科学基金项目

立项/批准年度： 2013

项目学科： 物理学II

项目作者： 李念北

作者单位： 同济大学

项目金额： 22万元

中文摘要： 作为非线性系统的代表性模型，一维非线性薛定谔方程晶格模型不但是统计物理领域一个广受研究的理想化模型，还准确的描述了实际物理系统，包括光学晶格中的有相互作用的冷原子气体和耦合非线性光波导管中的光波等等。在零噪声背景下，能量在一维非线性薛定谔方程晶格模型中的输运问题得到了广泛的研究，由于非线性、离散性以及无序性的相互影响，产生了诸如能量自陷、能量欠扩散等奇特能量输运行为。在更接近现实环境的热噪声背景下的能量输运问题，由于其相对的复杂性，相关的理论研究还没有开展。另一方面，热噪声背景下一维非线性原子链晶格模型能量输运的研究已经比较成熟，并发展出了不少卓有成效的数值计算方法和理论预测。本项目将致力于两个方面的工作，一是将原子链模型中最新发展的计算方法运用到薛定谔模型中，研究能量在热噪声、非线性、离散性以及无序性相互影响下的输运行为；二是在薛定谔模型中验证那些不依赖具体模型的有关能量输运的理论预测。

中文关键词： 能量输运；非线性薛定谔方程；能量扩散；平衡态统计力学；非线性动力学

英文摘要： As a paradigmatic model describing nonlinear phenomena,1D discrete nonlinear Schroedinger equation lattice model not only represents a most studied, idealized model in statistical physics, but also can be directly applied to experimental setups such as interacting cold atoms trapped in periodical optical lattices and coupled nonlinear waveguide arrays. Under zero noise background, the energy transfer in 1D discrete nonlinear Schroedinger equation lattice model has been intensively investigated. Due to the interplay among nonlinearity, discreteness and/or disorder, many novel behavior such as self-trapping, subdiffusion have been discovered. In stark contrast, the energy transfer under finite thermal noise background has not yet been tackled owing to the relative complexity introduced by thermal noise. On the other hand, the energy transfer under thermal noise in 1D nonlinear atomic lattice models is quite mature and some excellent simulation methods and theoretical predictions have been developed. Therefore, this project will focus on two parts: (1) we will apply the already proved simulation methods developed in atomic models to Schroedinger lattice models, in order to explore the energy transfer behavior influenced by the interplay among thermal noise, nonlinearity, discreteness and/or disorder. (2) we wil

英文关键词： Energy transport；Nonlinear Schrodinger equation；Energy diffusion；Equilibrium statistical mechanics；Nonlinear dynamics