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...

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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
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author Lin Wang
Jian Zu
author_facet Lin Wang
Jian Zu
author_sort Lin Wang
collection DOAJ
description 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.
format Article
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institution Kabale University
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publishDate 2020-01-01
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spelling doaj-art-5f061b7dbd0e45e1b1fb0ded2274930c2025-08-20T03:34:24ZengWileyAdvances in Mathematical Physics1687-91201687-91392020-01-01202010.1155/2020/25493072549307High-Order Approximation to Two-Level Systems with Quasiresonant ControlLin Wang0Jian Zu1School of Mathematics and Statistics, Changchun University of Technology, Changchun 130012, ChinaSchool of Mathematics and Statistics, & Center for Mathematics and Interdisciplinary Sciences, Northeast Normal University, Changchun 130024, ChinaIn 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.http://dx.doi.org/10.1155/2020/2549307
spellingShingle Lin Wang
Jian Zu
High-Order Approximation to Two-Level Systems with Quasiresonant Control
Advances in Mathematical Physics
title High-Order Approximation to Two-Level Systems with Quasiresonant Control
title_full High-Order Approximation to Two-Level Systems with Quasiresonant Control
title_fullStr High-Order Approximation to Two-Level Systems with Quasiresonant Control
title_full_unstemmed High-Order Approximation to Two-Level Systems with Quasiresonant Control
title_short High-Order Approximation to Two-Level Systems with Quasiresonant Control
title_sort high order approximation to two level systems with quasiresonant control
url http://dx.doi.org/10.1155/2020/2549307
work_keys_str_mv AT linwang highorderapproximationtotwolevelsystemswithquasiresonantcontrol
AT jianzu highorderapproximationtotwolevelsystemswithquasiresonantcontrol