Semiclassical Methods for the Evolution of Nonequilibrium Systems Undergoing Quantum Transitions

在这个由化学部理论和计算化学计划资助的项目中，Herman将开发高效和精确的半经典方法来评估非平衡凝聚相、气相和分子束系统中的量子跃迁几率和关联函数。这些密度演化方法只需要在量子相干度损失的数量级上考虑演化的全量子本质。这些方法是系统可纠正的，并提供了每个近似级别的计算误差的估计。这些程序将在可以获得精确量子结果的简单模型问题上进行测试，然后在可以获得实验数据的问题上进行测试。使用这些方法的计算结果也将与使用其他计算方法得到的结果进行比较。在实验方法能够描述越来越快的过程的时候，发展能够描述这种过程的理论形式是当务之急。这里提出的工作满足了这一需求。它还有望为分析和解释激发态系统中的超快非平衡过程提供一个框架。计划将这些方法扩展到远离平衡的系统，这将允许模拟新的化学反应类别。

In this project funded by the Theoretical and Computational Chemistry Program of the Chemistry Division, Herman will develop numerically efficient and accurate semiclassical methods to evaluate quantum transition probabilities and correlation functions in nonequilibrium condensed-phase, gas-phase, and molecular-beam systems. These density-evolution methods require consideration of the full quantum nature of the evolution only for times on the order of the loss of quantum phase coherence. These methods are systematically correctable and provide an estimate of the calculational error at each level of approximation. The procedures will be tested on simple model problems for which exact quantum results can be obtained and then on problems for which experimental data is available. The results of calculations using these methods will also be compared with those obtained using other computational methods.At a time when experimental methods are able to characterize increasingly fast processes, it is imperative to develop theoretical formalisms that are capable of describing such processes. The work proposed here addresses that need. It further promises to provide a framework for analyzing and interpreting ultra-fast nonequilibrium processes in excited-state systems. The planned extension of the methods to systems that are far from equilibrium will allow simulation of new classes of chemical reactions.