Jung Kenneth A, Videla Pablo E, Batista Victor S
Department of Chemistry, Yale University, P.O. Box 208107, New Haven, Connecticut 06520-8107, USA.
J Chem Phys. 2020 Sep 28;153(12):124112. doi: 10.1063/5.0021843.
Based on a recently developed generalization of Matsubara dynamics to the multi-time realm, we present a formal derivation of multi-time generalizations of ring-polymer molecular dynamics, thermostatted ring-polymer molecular dynamics (TRPMD), centroid molecular dynamics (CMD), and mean-field Matsubara dynamics. Additionally, we analyze the short-time accuracy of each methodology. We find that for multi-time correlation functions of linear operators, (T)RPMD is accurate up to order t, while CMD is only correct up to t, indicating a degradation in the accuracy of these methodologies with respect to the single-time counterparts. The present work provides a firm justification for the use of path-integral-based approximations for the calculation of multi-time correlation functions.
基于最近将松原动力学推广到多时间领域的研究成果，我们给出了环聚合物分子动力学、恒温环聚合物分子动力学（TRPMD）、质心分子动力学（CMD）和平均场松原动力学的多时间推广的形式推导。此外，我们分析了每种方法的短时精度。我们发现，对于线性算符的多时间关联函数，（T）RPMD在t阶以内是精确的，而CMD仅在t阶以内正确，这表明这些方法相对于单时间对应方法的精度有所下降。本工作为使用基于路径积分的近似方法来计算多时间关联函数提供了有力的依据。
