High-Order Approximation to Two-Level Systems with Quasiresonant Control
Keyword(s):
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.
2012 ◽
Vol E95.A
(10)
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pp. 1676-1682
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2013 ◽
Vol 47
(3)
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pp. 807-835
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2015 ◽
Vol 300
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pp. 423-437
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2013 ◽
Vol 37
(5)
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pp. 2802-2815
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2009 ◽
Vol 79
(17)
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pp. 1823-1828
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