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

Abstract EN

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.