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中对初始状态的记忆。虽然这个问题在经典系统中非常复杂，但事实证明，可以识别出一类有限的量子系统，对其进行相对简单的定量预测。这个项目致力于工作的例子。第一个是导轨中的两个原子。第二个由一个晶格上的五个二维强相互作用原子组成。第三种是由两个耦合陷阱中的原子组成的双组分混合物。在所有三种情况下，该小组都将测试一个简单的公式，该公式将松弛后可观测到的值从初始激发状态与它们的初始值联系起来。更广泛的影响：该项目本质上是跨学科的，位于原子、多体和数学物理、非线性科学和复杂系统之间的界面上。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[量子力学的量级，世界科学，c.2010]，致力于定性方法，这是许多人使用的一套技能，但没有人教过。

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.