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High-Order Approximation to Two-Level Systems with Quasiresonant Control

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  • Lin Wang
  • Jian Zu

Abstract

In this paper, we focus on high-order approximate solutions to two-level systems with quasi-resonant control. Firstly, we develop a high-order renormalization group (RG) method for Schrödinger equations. By this method, we get the high-order RG approximate solution in both resonance case and out of resonance case directly. Secondly, we introduce a time transformation to avoid the invalid expansion and get the high-order RG approximate solution in near resonance case. Finally, some numerical simulations are presented to illustrate the effectiveness of our RG method. We aim to provide a mathematically rigorous framework for mathematicians and physicists to analyze the high-order approximate solutions of quasi-resonant control problems.

Suggested Citation

  • Lin Wang & Jian Zu, 2020. "High-Order Approximation to Two-Level Systems with Quasiresonant Control," Advances in Mathematical Physics, Hindawi, vol. 2020, pages 1-10, October.
    • Handle: RePEc:hin:jnlamp:2549307
    DOI: 10.1155/2020/2549307
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