AI 中文总结
该研究针对一般量子态能量层级形成的动力学机制问题，提出量子朗道-利夫希茨-吉尔伯特动力学下，非线性量子耗散可从一般初始混合态本征涌现类似构造原理的能级序，为低能子空间选择性制备提供了途径。
AI 中文摘要
能量有序占据深深植根于量子物理中，从支配原子和分子中电子态填充的构造原理（Aufbau principle）到量子多体系统中低能构型的涌现皆是如此。然而，一般量子态如何形成这种能量层级的动力学机制仍是一个基础问题。本文表明，这种能量层级可从非线性量子耗散中动力学涌现，它并非作为原理被施加，也非通过与热库耦合产生，而是在量子朗道-利夫希茨-吉尔伯特（Landau-Lifshitz-Gilbert）动力学下，从一般初始混合态中本征涌现出类似构造原理的能级序。这种收敛是李雅普诺夫单调性与无序布居构型不稳定性的非平凡结果，所得动力学确立了一种组织密度矩阵布居的本征非线性机制，为低能子空间的选择性制备提供了途径，数值模拟验证了分析预测并展示了向低能扇区的收敛。
英文摘要
Energy-ordered occupation is deeply embedded in quantum physics, from the Aufbau principle governing the filling of electronic states in atoms and molecules to the emergence of low-energy configurations in quantum many-body systems. However, the dynamical mechanism by which a generic quantum state develops such an energy hierarchy remains a fundamental question. Here we show that such an energy hierarchy can emerge dynamically from nonlinear quantum dissipation. Rather than being imposed as a principle or generated through coupling to a thermal reservoir, an Aufbau-like ordering of energy levels emerges intrinsically under quantum Landau-Lifshitz-Gilbert dynamics from a generic initial mixed state. This convergence is a nontrivial consequence of Lyapunov monotonicity and instability of disordered population configurations. The resulting dynamics establish an intrinsic nonlinear mechanism for organizing density-matrix populations and provides a route toward selective preparation of low-energy subspaces. Numerical simulations confirm analytical predictions and illustrate convergence toward low-energy sectors.
