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

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...

Full description

Saved in:
Bibliographic Details
Main Authors: Lin Wang, Jian Zu
Format: Article
Language:English
Published: Wiley 2020-01-01
Series:Advances in Mathematical Physics
Online Access:http://dx.doi.org/10.1155/2020/2549307
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:1687-9120
1687-9139