Theory of Quantum Transitions

P. Kamenov

Quanlin Liu

Radiative transitions are quantum-state transitions in matter quantum systems (such as atoms， ions， and molecules) caused by their interaction with the electromagnetic field， and accompanied by the emission or absorption of photons.Their theoretical description involves physical theories including quantum mechanics and quantum electrodynamics， as well as mathematical tools such as spherical tensors and group theory.Focusing on radiative transitions of doped ions in solids， this paper summarizes earlier related theories and aims to concisely introduce fundamental theories and mathematical expressions while maintaining rigor， and to clearly describe the underlying physical pictures and mechanisms.The topics covered include atomic quantum states， the quantized electromagnetic field， multipole radiative transitions and selection rules， stimulated absorption， stimulated emission and spontaneous emission， transition probability and excited-state lifetimes.The article also discusses f-f and 4f-5d transitions of rare-earth ions and dd transitions of transition-metal ions， involving Judd -Ofelt theory， crystal-field theory， electronvibration coupling， and the Dorenbos model， as well as statistical analysis， machine learning， and firstprinciples methods.This work may provide a theoretical reference for the study of rare-earth-and transition-metaldoped luminescent materials.Keywords： radiative transition； theory； physical picture； f-f transition； d-d transition； 4f-5d transition 文章编号： 1000-7032(XXXX)XX

Jincheng Zhang

Quantum Phase Transition Theory (QPTT) offers a novel perspective on complex system behavior by explicitly modeling quantum state transitions. This paper investigates the application of QPTT to understanding systems undergoing significant change in their quantum states, specifically focusing on the optimization of quantum devices and systems, with a particular emphasis on the advancement of quantum computing and quantum communication. The core claim is to establish a robust model for QPTT, enabling the design of quantum devices and systems through iterative optimization strategies. This research explores the potential of QPTT to provide a deeper understanding of system dynamics and offers a novel approach to optimizing quantum components. The study will highlight the importance of this framework in the context of quantum technologies, providing a foundation for future advancements.

Sungbin Lim, Roslan Abd-Shukor, K. H. Kwek

Всеволод Феликсович Гантмахер, Valerii T. Dolgopolov

Metal--insulator transitions and transitions between different quantum Hall liquids are used to describe the physical ideas forming the basis of quantum phase transitions and the methods of application of theoretical results in processing experimental data. The following two theoretical schemes are discussed and compared: the general theory of quantum phase transitions, which has been developed according to the theory of thermodynamic phase transitions and relies on the concept of a partition function, and a theory which is based on a scaling hypothesis and the renormalization-group concept borrowed from quantum electrodynamics, with the results formulated in terms of flow diagrams.