| THE PHYSICS OF ELEMENTARY PARTICLES AND FIELDS |
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Finding Short-Range Parity-Time Phase-Transition Points with a Neural Network |
| Songju Lei1, Dong Bai2*, Zhongzhou Ren2,3*, and Mengjiao Lyu4,5 |
1School of Physics, Nanjing University, Nanjing 210093, China
2School of Physics Science and Engineering, Tongji University, Shanghai 200092, China
3Key Laboratory of Advanced Micro-Structure Materials (Ministry of Education), Shanghai 200092, China
4College of Science, Nanjing University of Aeronautics and Astronautics (NUAA), Nanjing 210016, China
5Key Laboratory of Aerospace Information Materials and Physics (NUAA), MIIT, Nanjing 211106, China
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| Cite this article: |
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Songju Lei, Dong Bai, Zhongzhou Ren et al 2021 Chin. Phys. Lett. 38 051101 |
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Abstract The non-Hermitian $PT$-symmetric system can live in either unbroken or broken $PT$-symmetric phase. The separation point of the unbroken and broken $PT$-symmetric phases is called the $PT$-phase-transition point. Conventionally, given an arbitrary non-Hermitian $PT$-symmetric Hamiltonian, one has to solve the corresponding Schrödinger equation explicitly in order to determine which phase it is actually in. Here, we propose to use artificial neural network (ANN) to determine the $PT$-phase-transition points for non-Hermitian $PT$-symmetric systems with short-range potentials. The numerical results given by ANN agree well with the literature, which shows the reliability of our new method.
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Received: 07 January 2021
Published: 02 May 2021
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| Fund: Supported by the National Natural Science Foundation of China (Grant Nos. 11535004, 11975167, 11761161001, 11375086, 11565010, 11881240623 and 11961141003), the National Key R&D Program of China (Grant Nos. 2018YFA0404403 and 2016YFE0129300), the Science and Technology Development Fund of Macau (Grant No. 008/2017/AFJ), and the Fundamental Research Funds for the Central Universities (Grant Nos. 22120210138 and 22120200101). |
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