Mathematical Sciences: The Discrete Self-Trapping Equation

本项目是一个研究离散自陷(DST)方程的项目。这个方程可以作为应用科学中许多重要效应的模型，从晶体中的电荷传输到蛋白质动力学。回顾了经典DST方程的基本性质，并概述了一个简单的量子过程。建议的研究包括：i)研究表现为非谐性增加的相变，ii)多自由度DST的研究，iii)确定DST中的非谐性对“Anderson局域化”的影响，以及iv)应用量子理论计算溶液轨迹的功率谱。

This project represents a research program to study the discrete self-trapping (DST) equation. This equation serves as a model for many important effects in applied science ranging from charge transport in crystals to protein dynamics. Basic properties of the classical DST equation are reviewed and a straightforward quantum procedure is outlined. The proposed research includes: i) Study of a phase transition that appears as anharmonicity is increased, ii) Study of DST for many degrees of freedom, iii) Determination of the effects of anharmonicity in DST on "Anderson localization", and iv) Applications of the quantum theory to compute power spectra of solution trajectories.