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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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| 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 |
| id | doaj-art-5f061b7dbd0e45e1b1fb0ded2274930c |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| 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 |