Woźniak D, Kalka M, Kołaczek D, Wołoszyn M, Spisak B J
Faculty of Physics and Applied Computer Science, AGH University of Krakow, al. Mickiewicza 30, 30-059, Kraków, Poland.
Department of Applied Mathematics, University of Agriculture in Kraków, ul. Balicka 253c, 30-198, Kraków, Poland.
Sci Rep. 2024 Dec 28;14(1):31294. doi: 10.1038/s41598-024-82744-6.
The concept of the symplectic covariance property of the Wigner distribution function and the symplectic invariance of the Wigner-Rényi entropies has been leveraged to estimate the interaction time of the moving quantum state in the presence of an absolutely integrable time-dependent potential. For this study, the considered scattering centre is represented initially by the Gaussian barrier. Two modifications of this potential energy are considered: a sudden change from barrier to barrier and from barrier to well. The scattering state is prepared in the form of a Schrödinger cat, and the Moyal equation governs its further time evolution. The whole analysis of the considered scattering problem is conducted in the above-barrier regime using the phase-space representation of quantum theory. The presented concept shifts the focus from the dynamics of the quantum state to a symplectically invariant state functions in the form of the Wigner-Rényi entropies of order one and one-half. These quantities serve as indicators of the beginning and end of the interaction of the non-Gaussian state with the sufficiently fast decaying potential representing the scattering centre. The presented approach is significant because it provides a new way to estimate the interaction time of moving quantum states with the dynamical scattering centre. Moreover, it allows for studying scattering processes in various physical systems, including atoms, molecules, and condensed matter systems.
维格纳分布函数的辛协方差性质以及维格纳 - 雷尼熵的辛不变性这一概念，已被用于在存在绝对可积的含时势的情况下估计移动量子态的相互作用时间。在本研究中，所考虑的散射中心最初由高斯势垒表示。考虑了这种势能的两种修改：从势垒到势垒以及从势垒到势阱的突然变化。散射态以薛定谔猫态的形式制备，并且莫亚方程支配其进一步的时间演化。使用量子理论的相空间表示，在势垒上方区域对所考虑的散射问题进行了整体分析。所提出的概念将焦点从量子态的动力学转移到以一阶和二分之一阶维格纳 - 雷尼熵形式的辛不变态函数。这些量用作非高斯态与代表散射中心的充分快速衰减势相互作用开始和结束的指标。所提出的方法具有重要意义，因为它提供了一种估计移动量子态与动态散射中心相互作用时间的新方法。此外，它允许研究各种物理系统中的散射过程，包括原子、分子和凝聚态物质系统。
