发表机构
Uppsala University; Universität Siegen（乌普萨拉大学; 锡根大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究非绝热量子时间演化中沿复格拉斯曼流形回路子空间的准全纯性，通过分解薛定谔演化，获依赖动力学传播子的有效几何生成元，探讨多种分解方式及相关问题。
AI 中文摘要
我们为复格拉斯曼流形中沿回路的子空间非绝热量子时间演化的准全纯性发展了一个框架。通过在移动基中将薛定谔演化分解为动力学和连接诱导贡献，我们得到了一个明确依赖于动力学传播子的有效几何生成元。这个准连接在原始格拉斯曼丛上并不定义一个真正的连接，因为它的规范变换律获得了一个依赖历史的非局部项。还简要讨论了分解薛定谔演化的其他方法。所有这些方法都存在相同类型的历史依赖性，从而定义了子空间的传输，其中几何和动力学效应通常相互交织，就像准全纯性的情况一样。我们的工作从本质上的规范理论角度阐明了将子空间的量子演化分离为全纯和动力学部分的问题。
英文摘要
We develop a framework for quasi-holonomy in non-adiabatic quantum time evolution of subspaces along loops in a complex Grassmannian. By factoring the Schrödinger evolution into dynamical and connection-induced contributions in a moving basis, we obtain an effective geometric generator that depends explicitly on the dynamical propagator. This quasi-connection does not define a genuine connection on the original Grassmann bundle, since its gauge transformation law acquires a history-dependent, nonlocal term. Other ways of factoring the Schrödinger evolution are briefly discussed. All these approaches suffer from the same type of history-dependence, thereby defining transport of subspaces in which geometric and dynamical effects are generally intertwined, just as in the case of the quasi-holonomy. Our work sheds light on the issue of separating quantum evolution of subspaces into holonomic and dynamical parts from an essentially gauge-theoretic perspective.
CommentsMinor change; journal reference added
Journal refJ. Phys. A: Math. Theor. 59, 355308 (2026)
