标题： 混合Weyl符号演算与光谱线型理论 显示英文标题

标题： Mixed Weyl Symbol Calculus and Spectral Line Shape Theory

摘要： 一个新的且计算上可行的全量子版本的线型理论通过混合魏尔符号演算获得。 碰撞展宽线型理论的基本要素是辐射体-扰动子系统的时变偶极自相关函数。 观测到的光谱强度是该相关函数的傅里叶变换。 为了描述该系统的量子结构，引入了量子算符与相空间函数（魏尔符号）之间威格纳-魏尔同构的一种修改形式。 这种修改使用部分威格纳变换，其中辐射体-扰动子相对运动自由度被转换为相空间依赖性，而与内部分子自由度相关的算符则保持在它们原来的希尔伯特空间形式。 这种部分威格纳变换的结果被称为混合魏尔符号。 确定了混合魏尔符号演算特有的星积、莫耶括号和渐近展开。 相关函数表示为相空间积分中两个混合符号之积：一个对应于系统初始构型，另一个为其时间演化动力学值。 在这个方法中有两种半经典展开——一种与扰动子散射过程有关，另一种与混合符号的星积有关。 这些近似结合使用以获得自相关函数的足够简单的表示形式，从而允许数值计算。 首阶O(\hbar ^0)近似恢复标准的经典路径近似用于线型。 高阶O(\hbar ^1)修正来源于星积的非交换性质。 显示英文摘要

摘要： A new and computationally viable full quantum version of line shape theory is obtained in terms of a mixed Weyl symbol calculus. The basic ingredient in the collision--broadened line shape theory is the time dependent dipole autocorrelation function of the radiator-perturber system. The observed spectral intensity is the Fourier transform of this correlation function. A modified form of the Wigner--Weyl isomorphism between quantum operators and phase space functions (Weyl symbols) is introduced in order to describe the quantum structure of this system. This modification uses a partial Wigner transform in which the radiator-perturber relative motion degrees of freedom are transformed into a phase space dependence, while operators associated with the internal molecular degrees of freedom are kept in their original Hilbert space form. The result of this partial Wigner transform is called a mixed Weyl symbol. The star product, Moyal bracket and asymptotic expansions native to the mixed Weyl symbol calculus are determined. The correlation function is represented as the phase space integral of the product of two mixed symbols: one corresponding to the initial configuration of the system, the other being its time evolving dynamical value. There are, in this approach, two semiclassical expansions -- one associated with the perturber scattering process, the other with the mixed symbol star product. These approximations are used in combination to obtain representations of the autocorrelation that are sufficiently simple to allow numerical calculation. The leading O(\hbar^0) approximation recovers the standard classical path approximation for line shapes. The higher order O(\hbar^1) corrections arise from the noncommutative nature of the star product.