AI 中文总结
本文针对作为量子科学核心对象的投影系综，建立了其动力学的通用精确非平衡理论，推导了相关方程并给出经典表示，为其多方面研究提供了分析框架，应用广泛。
AI 中文摘要
投影系综是通过测量纠缠环境在系统上诱导的条件纯态集合，已成为量子科学的核心研究对象，是深度热化、量子态设计、经典性涌现的基础，且展现出有趣的相变现象。本文建立了其动力学的通用精确理论，为投影系综的动力学、平衡态及非平衡稳态提供了系统方法。我们推导了量子态空间上针对投影系综的精确连续性方程，以及由系统-环境相互作用产生的微观动力学方程、概率通量和源项的解析表达式。所得动力学可呈现经典形式：孤立系统服从哈密顿输运与刘维尔定理，开放系统则由概率输运的动力学理论描述。稳态连续性方程为平衡态与非平衡稳态投影系综提供了通用表征，可通过特征线法分析。该理论为研究平衡态与非平衡稳态投影系综的涌现、结构及时标提供了分析框架，应用范围涵盖深度热化、经典性涌现、随机量子态生成及量子器件基准测试等领域。
英文摘要
Projected ensembles---the collections of conditional pure states induced on a system by measuring an entangled environment---have become central objects in quantum science, underlying deep thermalization, quantum state designs, the emergence of classicality, and exhibiting interesting phase transitions. Here we develop a general and exact theory of their dynamics, yielding a systematic approach to their dynamics and equilibrium and non-equilibrium stationary states. We derive an exact continuity equation on quantum state space for the projected ensemble, together with microscopic kinetic equations and analytical expressions for the probability flux and source terms generated by the system-environment interaction. The resulting dynamics admits a classical representation: isolated systems obey Hamiltonian transport and Liouville's theorem, while open systems are described by a kinetic theory of probability transport. The stationary continuity equation provides a general characterization of equilibrium and non-equilibrium stationary projected ensembles, which can be analyzed through the method of characteristics. The theory provides an analytical framework for studying the emergence, structure, and timescales of equilibrium and non-equilibrium stationary projected ensembles, with applications ranging from deep thermalization and the emergence of classicality to random quantum-state generation and quantum device benchmarking.
Comments17 pages, 4 figures
