Dynamics and Spectroscopy in the Semiclassical and Extreme Quantum Regimes

半经典和极端量子体系中的动力学和光谱学

• 批准号: 9610501
• 负责人: Eric Heller
• 金额: $ 46.27万
• 依托单位: Harvard University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1997
• 资助国家: 美国
• 起止时间: 1997-05-15 至 2000-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9610501&HistoricalAwards=false
• 关键词: Dynamics; Spectroscopy; Semiclassical; Extreme; Quantum

*** 9610501 HELLER The Theoretical and Computational Ahemistry program is supporting Professor Eric Heller at Harvard University to work on scattering theory. First, Heller will take a new look at scattering theory at extremely low energies. This regime has become important because of laser cooling and trapping of atoms, as well as carrier gas cooling and trapping of molecules. In this "cold collision" regime, Heller will study ultra-low energy, three-atom collisions and recombination (molecule formation), proximity resonances, which are a new class of low energy multiple scattering resonances related to Efimov states, and ultra-low energy molecule-molecule collisions, with an eye to the formation of long lived resonances. Common to these areas is the concept of "boundary condition engineering," wherein the effect of short range potentials can in fact be ascribed to a change in boundary conditions on the wavefunction. In a related study Heller will extend and apply the theory of multiple scattering and conductance in "quantum corrals" and other arrangements or arrays of atoms into walls and sheets. He will also investigate novel approaches to dynamical tunneling in polyatomic molecules, and its effect on high resolution spectra, deflection of beams in inhomogeneous fields, and quantum control in Landau-Zener crossing. This work, like the ultra-low energy scattering theory above, addresses the extreme quantum regime. In a second class of problems, at the opposite end of the scale at higher energy, Heller will extend his fundamental research in semiclassical approximations to chaotic systems to include the theory of scarring by classical periodic orbits and semiclassical quantization of chaos. In particular he is looking for an appropriate nonlinear theory of wavefunction scarring. Finally this work will undertake several projects involving fundamental issues of quantization, including quantization on constrained non-Euclidian spac es, and quantization of chaos in maps such as the whisker map. This research involves fundamental studies of quantum mechanics, and the profound effects quantum mechanics has on matter, as energy is lowered almost to absolute zero. At very low temperatures, matter wave-like behavior dominates over particle-like behavior. Wavelengths get extremely long. The waves have to obey "boundary conditions," which are rules on how the waves behave when one atom or molecule approaches another, or approaches a wall. At ultra-low energies these boundary conditions are uncommonly important, often determining the way the matter behaves. In this strange "tail wagging the dog" regime, anything that can be done to change the boundary conditions may have profound effects. For example, normal boundary conditions in quantum mechanics forces minimum energy upon the system known as the zero point energy. Removing the zero point energy, by using walls made of special atoms, may drastically affect the usefulness of small devices such as wires, and may profoundly affect the outcome of the slow collision of two cold molecules. Related work involves the issue of quantization; that is, how do we take a given system and correctly endow it with the proper quantum behavior. There are rules on how to do this in simple cases but the rules are ambiguous when constraints are present, for example (requiring that a given bond length to be a certain fixed value). Heller is developing some ideas which bootstrap the ambiguous cases as limits of the easy cases, thus removing the ambiguity. ***

*** 9610501 HELLER理论和计算阿姆斯壮程序支持 哈佛大学的埃里克·海勒教授研究散射理论。 首先，海勒将采取新的眼光在散射理论在极低 能量 由于激光冷却，这种制度变得很重要， 捕获原子，以及载气冷却和捕获 分子。 在这种“冷碰撞”制度下，海勒将研究超低 能量，三原子碰撞和复合（分子形成）， 邻近共振，这是一类新的低能量多 与Efimov态相关的散射共振和超低能量 分子-分子碰撞，着眼于形成长寿命的 共振 这些领域的共同点是“边界条件”的概念 工程，”其中短程电位的影响实际上可以是 归因于波函数边界条件的变化。 中 相关研究海勒将扩展和应用理论的多重 “量子相干”和其他安排中的散射和电导， 排列成墙和薄片。 他还将调查小说 多原子分子中动力学隧穿的方法及其效应 在高分辨率光谱上，不均匀场中的光束偏转， 和量子控制。 这项工作，就像 超低能量散射理论，解决了极端的量子 政权 在第二类问题中，处于天平的另一端 在更高的能量，海勒将扩大他的基础研究， 混沌系统的半经典逼近，包括 疤痕的经典周期轨道和半经典量子化 混沌 特别是他正在寻找一个适当的非线性理论 波函数疤痕 最后，这项工作将进行几个 涉及量化基本问题的项目，包括 约束非欧几里德空间上的量子化，以及 像触须地图这样的地图中的混沌。 这项研究涉及量子力学的基础研究， 量子力学对物质有着深远的影响， 接近绝对零度 在非常低的温度下，物质像波一样 行为优于类粒子行为。 韦弗尔勒盖特 非常长。 波必须服从“边界条件”， 当一个原子或分子靠近时波的行为规则 另一个，或接近一堵墙。 在超低能量下，这些边界 条件是非常重要的，往往决定了事情的方式， 行为。 在这种奇怪的“尾巴摇狗”制度下，任何 改变边界条件可能会产生深远的影响。 例如，量子力学中的正常边界条件 系统的最小能量称为零点能量。 去除 零点能量，通过使用由特殊原子构成的壁， 极大地影响了诸如电线之类的小型设备的有用性，并且 可能会深刻地影响两个寒冷星球缓慢碰撞的结果 分子。 相关的工作涉及到量化的问题;也就是说， 我们是否可以给一个给定的系统赋予适当的量子 行为 在简单的情况下，有关于如何做到这一点的规则，但 当存在约束时，规则是模糊的，例如（要求 即给定的键长为某一固定值）。 海勒是 发展了一些想法，这些想法将模棱两可的情况作为限制， 简单的情况下，从而消除歧义。 ***