Dynamics and Spectroscopy in the Semiclassical and Extreme Quantum Regimes

*9610501海勒理论和计算化学项目正在支持哈佛大学的埃里克·海勒教授从事散射理论的工作。首先，海勒将重新审视极低能量下的散射理论。由于激光冷却和捕获原子，以及载气冷却和捕获分子，这一制度变得重要起来。在这种“冷碰撞”机制中，海勒将研究超低能量、三原子碰撞和重组(分子形成)、邻近共振，这是一类与Efimov态有关的新的低能量多重散射共振，以及超低能量分子-分子碰撞，着眼于形成长寿命共振。这些地区的共同之处是“边界条件工程”的概念，其中短程电势的影响实际上可以归因于边界条件对波函数的改变。在一项相关的研究中，海勒将把多重散射和电导理论扩展和应用到“量子围栏”和其他原子排列或阵列中，形成墙壁和薄片。他还将研究多原子分子中动态隧穿的新方法，以及它对高分辨率光谱的影响，光束在非均匀场中的偏转，以及Landau-Zener交叉中的量子控制。这项工作，就像上面的超低能量散射理论一样，解决了极端的量子制度。在第二类问题中，在更高能量的尺度的另一端，Heller将扩展他对混沌系统的半经典逼近的基础研究，包括经典周期轨道的伤疤理论和混沌的半经典量子化。特别是，他正在寻找一种合适的波函数疤痕非线性理论。最后，这项工作将承担几个涉及量子化基本问题的项目，包括约束非欧几里得空间上的量子化，以及诸如晶须映射等映射中的混沌的量子化。这项研究涉及量子力学的基础研究，以及量子力学对物质的深刻影响，因为能量几乎降至绝对零度。在很低的温度下，物质波的行为比粒子的行为更占优势。波长变得非常长。波必须遵守“边界条件”，即当一个原子或分子接近另一个原子或分子或接近墙壁时，波的行为规则。在超低能量下，这些边界条件非常重要，通常决定了物质的行为方式。在这个奇怪的“摇尾巴”政权中，任何可以改变边界条件的事情都可能产生深远的影响。例如，量子力学中的正常边界条件迫使系统获得最小能量，称为零点能量。通过使用由特殊原子制成的墙来消除零点能量，可能会极大地影响电线等小型设备的用途，并可能深刻影响两个冷分子缓慢碰撞的结果。相关工作涉及量子化的问题；也就是，我们如何获得一个给定的系统，并正确地赋予它适当的量子行为。在简单情况下如何做到这一点有一些规则，但当存在约束时，规则是含糊不清的，例如(要求给定的债券长度必须是某个固定值)。海勒正在发展一些想法，将模棱两可的案例作为简单案例的界限，从而消除歧义。***

*** 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. ***