High‐order long‐time approximation of (N + 1)‐level systems with near‐resonance control.
- Resource Type
- Article
- Authors
- Geng, Ru; Zu, Jian
- Source
- Mathematical Methods in the Applied Sciences. Feb2022, Vol. 45 Issue 3, p1224-1240. 17p.
- Subject
- *RENORMALIZATION group
*RUNGE-Kutta formulas
*COMPUTER simulation
- Language
- ISSN
- 0170-4214
In this paper, we focus on high‐order approximate solutions of (N + 1)‐level systems with near‐resonance control over a long period of time. A high‐order renormalization group (RG) method with rigorous proof is developed to deal with such open quantum systems. By constructing high‐order RG equations, we obtained the high‐order long‐time RG approximate solutions of (N + 1)‐level systems in several kinds of near‐resonance cases. The numerical simulation results show that our high‐order RG method has the same accuracy as the fourth‐order Runge–Kutta method in O(1) time scale but more reliable in O1ε time scale. [ABSTRACT FROM AUTHOR]