{"title":"The non-adiabatic sub-geometric phase and its application on quantum transition","authors":"Zheng-Chuan Wang","doi":"10.1140/epjd/s10053-025-00986-z","DOIUrl":null,"url":null,"abstract":"<div><p>Based on the adiabatic sub-geometric phase proposed for density matrix (Wang in Sci. Rep. 9: 13258, 2019), we further extend it to the non-adiabatic case. It is found that both the real and imaginary parts of the sub-geometric phase can play an important role in quantum transition. The imaginary part of sub-geometric phase can deviate the resonance peak in the quantum transition, and bring modification on the level crossing, while the real part of sub-geometric phase will determine the stability of initial state according to the linear stability analysis theory, which can be regarded as somewhat complement to the selection rule of quantum transition. Finally, we illustrate them by two examples: one is the system with time-dependent perturbation, another is a two-level system. It indicates that both the real and imaginary parts of sub-geometric phase have influences on the quantum transition.</p><h3>Graphical abstract</h3><p>We proposed a new sub-geometric phase in the non-adiabatic case for density matrix, which can be used to explore the quantum transition.</p><div><figure><div><div><picture><img></picture></div></div></figure></div></div>","PeriodicalId":789,"journal":{"name":"The European Physical Journal D","volume":"79 4","pages":""},"PeriodicalIF":1.5000,"publicationDate":"2025-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"The European Physical Journal D","FirstCategoryId":"4","ListUrlMain":"https://link.springer.com/article/10.1140/epjd/s10053-025-00986-z","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"OPTICS","Score":null,"Total":0}
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Abstract
Based on the adiabatic sub-geometric phase proposed for density matrix (Wang in Sci. Rep. 9: 13258, 2019), we further extend it to the non-adiabatic case. It is found that both the real and imaginary parts of the sub-geometric phase can play an important role in quantum transition. The imaginary part of sub-geometric phase can deviate the resonance peak in the quantum transition, and bring modification on the level crossing, while the real part of sub-geometric phase will determine the stability of initial state according to the linear stability analysis theory, which can be regarded as somewhat complement to the selection rule of quantum transition. Finally, we illustrate them by two examples: one is the system with time-dependent perturbation, another is a two-level system. It indicates that both the real and imaginary parts of sub-geometric phase have influences on the quantum transition.
Graphical abstract
We proposed a new sub-geometric phase in the non-adiabatic case for density matrix, which can be used to explore the quantum transition.
期刊介绍：
The European Physical Journal D (EPJ D) presents new and original research results in:
Atomic Physics;
Molecular Physics and Chemical Physics;
Atomic and Molecular Collisions;
Clusters and Nanostructures;
Plasma Physics;
Laser Cooling and Quantum Gas;
Nonlinear Dynamics;
Optical Physics;
Quantum Optics and Quantum Information;
Ultraintense and Ultrashort Laser Fields.
The range of topics covered in these areas is extensive, from Molecular Interaction and Reactivity to Spectroscopy and Thermodynamics of Clusters, from Atomic Optics to Bose-Einstein Condensation to Femtochemistry.
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