发表机构
National Sun Yat-sen University; National Center for Theoretical Sciences（国立中山大学; 国家理论科学中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究通过Wirtinger导数将演化生成器形式主义扩展到复值参数，推导了量子态和希尔伯特空间丛度量的演化方程，给出实例验证了其物理一致性。
AI 中文摘要
关于量子系统如何受外部因素影响的理论研究，常通过系统哈密顿量的参数变化来表述。除了聚焦特定哈密顿量本征态的Berry联络与Berry相位外，近期受非厄米量子形式主义启发的研究，提供了获取实值参数通用态演化生成器的框架。本研究通过Wirtinger导数将演化生成器形式主义的适用性扩展到复值参数。通过将复参数及其共轭视为独立变量，推导了量子态和希尔伯特空间丛度量的演化方程。分析表明，虽然关于复参数的态演化自然受其对应演化生成器的支配，但度量演化需要生成器与其共轭对应项的耦合贡献，以保持态归一化。本文给出了明确的实例，以说明该形式主义的实现方式和物理一致性。
英文摘要
Theoretical studies on how quantum systems are affected by external factors are often formulated through parameter changes in the system's Hamiltonian. Beyond Berry connections and phases, which focus on specific Hamiltonian eigenstates, recent studies inspired by non-Hermitian quantum formalisms provide a framework for obtaining general state evolution generators for real-valued parameters. This study extends the applicability of the evolution generator formalism to complex-valued parameters via Wirtinger derivatives. By treating a complex parameter and its conjugate as independent variables, the evolution equations are derived for both quantum states and the metric of the Hilbert space bundle. The analysis demonstrates that while state evolution with respect to a complex parameter is naturally governed by its corresponding evolution generator, metric evolution requires a coupled contribution from both the generator and its conjugate counterpart to preserve state normalization. Explicit examples are worked out to illustrate the implementation and physical consistency of the formalism.
