Quantum Nonequilibrium Dynamics

智力价值：这个项目的中心主题是在有序和混沌之间的量子系统的初始状态的记忆。虽然这个问题在经典系统中是非常复杂的，但事实证明，有可能识别出一类有限的量子系统，可以对其进行相对简单的定量预测。本项目致力于工作实例。第一个是两个原子在一个引导。第二种由晶格上的五个二维强相互作用原子组成。第三种是原子在两个耦合阱中的双组分混合物。在这三种情况下，该小组将测试一个简单的公式，该公式将从初始激发态弛豫后的可观测值与它们的初始值联系起来。更广泛的影响：跨学科的性质，该项目是原子，多体，数学物理，非线性科学和复杂系统之间的接口。它将为马萨诸塞大学波士顿分校的本科生和研究生提供分析和数值经验。PI还将编写一本面向本科生的书[量子力学的数量级，世界科学，c. 2010]，致力于定性方法，这是一套被许多人使用却没有教授的技能。

Intellectual Merit: The central theme of this project is the memory of the initial state in quantum systems in between order and chaos. While this question is immensely complicated in classical systems, it turns out to be possible to identify a limited class of quantum systems for which relatively simple quantitative predictions can be made. This project is devoted to worked examples. The first of them is two atoms in a guide. The second consists of five two-dimensional strongly interacting atoms on a lattice. The third is a two-component mixture of atoms in two coupled traps. In all three cases, the group will be testing a simple formula that relates the values of observables after relaxation from an initial excited state to their initial values. Broader impact: Interdisciplinary by nature, the project lies on the interface between Atomic,Many-Body, and Mathematical Physics, Nonlinear Science, and Complex Systems. It will provide analytical and numerical experience for undergraduate and graduate students at the University of Massachusetts Boston. The PI will also work on an undergraduate-oriented book [Quantum Mechanics by order of magnitude, World Scientific, c. 2010] devoted to qualitative methods, a set of skills used by many and taught nowhere.