Low-Storage Runge-Kutta Method for Simulating Time-Dependent Quantum Dynamics  

含时量子动力学模拟的低存储龙格-库塔方法

作　　者：严运安[1,2] 

机构地区：[1]贵州师范学院,贵州省纳米材料模拟与计算重点实验室,贵州550018 [2]北京计算科学研究中心,北京100094

出　　处：《Chinese Journal of Chemical Physics》2017年第3期277-286,I0001,共11页化学物理学报（英文）

基　　金：This work is supported by the National Natural Science Foundation of China （No.21373064）, the Program for Innovative Research Team of Guizhou Province （No.QKTD[2014]4021）, and the Natural Sci- entific Foundation from Guizhou Provincial Department of Education （No.ZDXK[2014]IS）. All the calculations were performed at Guizhou Provincial High- Performance Computing Center of Condensed Mate- rials and Molecular Simulation in Guizhou Education University.

摘　　要：A wide range of quantum systems are time-invariant and the corresponding dynamics is dic- tated by linear differential equations with constant coefficients. Although simple in math- ematical concept, the integration of these equations is usually complicated in practice for complex systems, where both the computational time and the memory storage become limit- ing factors. For this reason, low-storage Runge-Kutta methods become increasingly popular for the time integration. This work suggests a series of s-stage sth-order explicit Runge- Kutta methods specific for autonomous linear equations, which only requires two times of the memory storage for the state vector. We also introduce a 13-stage eighth-order scheme for autonomous linear equations, which has optimized stability region and is reduced to a fifth-order method for general equations. These methods exhibit significant performance improvements over the previous general-purpose low-stage schemes. As an example, we ap- ply the integrator to simulate the non-Markovian exciton dynamics in a 15-site linear chain consisting of perylene-bisimide derivatives.

关 键 词：Low-storage Runge-Kutta Autonomous linear differential equation Time-dependent dynamics Time-invariant Hamiltonian 

分 类 号：O[理学]