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Low-storage Runge-Kutta method for simulating time-dependent quantum dynamics
严运安
Author NameAffiliationE-mail
严运安 贵州师范学院 yunan@gznc.edu.cn 
Abstract:
A wide range of quantum systems are time-invariant and the corresponding dynamics is dictated by linear di erential equations with constant coecients. 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 Runge-Kutta methods speci c 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 fth-order method for general equations. These methods exhibit signi cant 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.
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Low-storage Runge-Kutta method for simulating time-dependent quantum dynamics
严运安
摘要:
A wide range of quantum systems are time-invariant and the corresponding dynamics is dictated by linear di erential equations with constant coecients. 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 Runge-Kutta methods speci c 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 fth-order method for general equations. These methods exhibit signi cant 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.
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