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Low-Storage Runge-Kutta Method for Simulating Time-Dependent Quantum Dynamics
Yun-an Yan*
Author NameAffiliationE-mail
Yun-an Yan* Guizhou Provincial Key Laboratory of Computational Nano-Material Science, Guizhou Education University, Guizhou 550018, China;Beijing Computational Science Research Center, Beijing 100094, China yunan@gznc.edu.cn 
Abstract:
A wide range of quantum systems are time-invariant and the corresponding dynamics is dictated by linear differential equations with constant coefficients.Although simple in mathematical concept,the integration of these equations is usually complicated in practice for complex systems,where both the computational time and the memory storage become limiting 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 RungeKutta 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 apply the integrator to simulate the non-Markovian exciton dynamics in a 15-site linear chain consisting of perylene-bisimide derivatives.
Key words:  Low-storage Runge-Kutta  Autonomous linear differential equation  Timedependent dynamics  Time-invariant Hamiltonian
FundProject: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 Scientific Foundation from Guizhou Provincial Department of Education (No.ZDXK[2014]18).All the calculations were performed at Guizhou Provincial HighPerformance Computing Center of Condensed Materials and Molecular Simulation in Guizhou Education University.
含时量子动力学模拟的低存储龙格-库塔方法
严运安*
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DOI:10.1063/1674-0068/30/cjcp1703025
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