发表机构
Max-Born-Institut; Technische Universität Berlin（马克斯·玻恩研究所; 柏林工业大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出手性转动波包概念，证明非手性分子可通过转动态叠加产生动力学手性轨迹，并引入几何与原点参考两种赝标量度量来量化手性，其中几何度量非零是真正手性的充分条件。
AI 中文摘要
我们引入了手性转动波包：非手性分子的少数低转动态的相干叠加，其中分子轴的期望值在实验室坐标系中描绘出一条三维手性曲线。手性是量子态的动力学性质而非平衡结构的性质，并且我们证明它可以被印记在线性转子上，以及球形和对称陀螺上。我们在Wigner $D^J_{MK}$基中推导了空间反演、运动反转及其乘积对这些波包的作用，并定义了给定波包的转动对映体。为了量化取向轨迹的手性，我们引入了两个基于导数的赝标量度量：一个是由轨迹的曲率和挠率构建的几何度量，它在运动反转下为偶；另一个是参考原点构建的度量，由副法线矢量构建，它在运动反转下为奇。后者被证明与轨迹投影到单位球面上的测地曲率成正比，这通过高斯-博内定理将其与投影轨迹所包围的立体角以及分子固定矢量的平行输运和乐联系起来。最后，我们证明非零几何度量是波包在巴伦意义上真正手性的充分条件，而具有实展开系数的波包仅为虚假手性。
英文摘要
We introduce chiral rotational wavepackets: coherent superpositions of a few low-lying rotational states of an achiral molecule for which the expectation value of a molecular axis traces a three-dimensional chiral curve in the laboratory frame. The handedness is a dynamical property of the quantum state rather than of the equilibrium structure, and we show that it can be imprinted on linear rotors as well as on spherical and symmetric tops. We derive the action of space inversion, motion reversal, and their product on such wavepackets in the Wigner $D^J_{MK}$ basis, and define the rotational enantiomers of a given wavepacket. To quantify the handedness of the orientation trajectory we introduce two derivative-based pseudoscalar measures: a geometrical measure built from the curvature and torsion of the trajectory, which is even under motion reversal, and an origin-referenced measure built from the binormal vector, which is odd under motion reversal. The latter is shown to be proportional to the geodesic curvature of the trajectory projected onto the unit sphere, which links it, via the Gauss--Bonnet theorem, to the solid angle enclosed by the projected trajectory and to the parallel-transport holonomy of a molecule-fixed vector. Finally we show that a nonzero geometrical measure is a sufficient condition for the wavepacket to be truly chiral in the sense of Barron, while wavepackets with real expansion coefficients are only falsely chiral.
