System analysis

Dexi Li

Quantum field theory is a physical theory that has a very complete system of mathematical forms. In order to reveal the meaning of quantum field theory,we need to analyze its form system syntactically. Moreover,we make such a semantic analysis of the theorem,formula and symbolic representation in its form system,so that the physical interpretation of form system can be achieved. In addition,the meaning of quantum field theory will be more complete and clear,and the subjective factors of the individuals who formalized quantum field theory will be revealed through a pragmatic analysis of its form system. As the central research method of contextualism,contextual analysis is a synthesis of syntactic analysis,semantic analysis and pragmatic analysis. Therefore,the contextual analysis of the quantum field theory can integrate the syntactic,the semantic and the pragmatic analysis,and so do the static analysis and dynamic analysis.

Ulrich Karrenberg

Takayuki Suzuki, Eiki Taniguchi, Kaito Iwamura

The dynamics of quantum systems under the adiabatic Hamiltonian has attracted attention not only in quantum control but also in a wide range of fields from condensed-matter physics to high-energy physics because of its nonperturbative behavior. Here we analyze the adiabatic dynamics in two-level systems and multilevel systems using exact WKB analysis, which is one of the nonperturbative analysis methods. As a result, we obtain a formula for the transition probability, which is similar to the known formula in the two-level system. Although nonperturbative analysis in the adiabatic limit has rarely been studied for multilevel systems, we show that the same analysis can be applied and also provide a concrete example. The results will serve as a basis for the application of exact WKB analysis in various fields of physics.

Ulrich Karrenberg

Jincheng Zhang

This paper introduces Hyper-Adaptive Symmetry Analysis (HASA), a novel algorithm for detecting and quantifying subtle, dynamically changing symmetry patterns across complex systems. Recognizing the limitations of traditional symmetry analysis, which often relies on static representations, we propose a flow-based approach that dynamically constructs a multi-scale representation of the system's structure, enabling the identification of patterns that evolve over time. The core mechanism leverages variational quantum computation (VQC) for rapid analysis of these dynamic symmetries. We demonstrate the effectiveness of HASA through rigorous simulations and preliminary analysis of [mention a specific system type, e.g., fluid dynamics simulations] exhibiting complex, evolving symmetry states. The algorithm's potential for uncovering previously hidden symmetry structures offers a significant advancement in the field of complex systems analysis.