Svensson S Karl-Mikael, Poulsen Jens Aage, Nyman Gunnar
Department of Chemistry and Molecular Biology, University of Gothenburg, SE 405 30 Gothenburg, Sweden.
J Chem Phys. 2020 Mar 7;152(9):094111. doi: 10.1063/1.5126183.
The classical Wigner model is one way to approximate the quantum dynamics of atomic nuclei. Here, a new method is presented for sampling the initial quantum mechanical distribution that is required in the classical Wigner model. The new method is tested for the position, position-squared, momentum, and momentum-squared autocorrelation functions for a one-dimensional quartic oscillator and double well potential as well as a quartic oscillator coupled to harmonic baths of different sizes. Two versions of the new method are tested and shown to possibly be useful. Both versions always converge toward the classical Wigner limit. For the one-dimensional cases, some results that are essentially converged to the classical Wigner limit are acquired and others are not far off. For the multi-dimensional systems, the convergence is slower, but approximating the sampling of the harmonic bath with classical mechanics was found to greatly improve the numerical performance. For the double well, the new method is noticeably better than the Feynman-Kleinert linearized path integral method at reproducing the exact classical Wigner results, but they are equally good at reproducing exact quantum mechanics. The new method is suggested as being interesting for future tests on other correlation functions and systems.
经典维格纳模型是近似原子核量子动力学的一种方法。本文提出了一种新方法，用于对经典维格纳模型所需的初始量子力学分布进行采样。该新方法针对一维四次方振子、双阱势以及耦合到不同大小谐波浴的四次方振子的位置、位置平方、动量和动量平方自相关函数进行了测试。对新方法的两个版本进行了测试，结果表明它们可能是有用的。两个版本均始终收敛于经典维格纳极限。对于一维情况，获得了一些基本收敛于经典维格纳极限的结果，其他结果也与之相差不远。对于多维系统，收敛速度较慢，但发现用经典力学近似谐波浴的采样可大大提高数值性能。对于双阱，在重现精确的经典维格纳结果方面，新方法明显优于费曼 - 克莱因特线性化路径积分方法，但在重现精确量子力学方面两者同样出色。建议新方法对于未来在其他相关函数和系统上的测试具有吸引力。
