非厄米量子力学 I：瞬时自能
Non-Hermitian Quantum Mechanics I: Instantaneous Self-Energy
- Xiamen University（厦门大学）
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所）
- New Cornerstone Science Laboratory（新基石科学实验室）
- Asia Pacific Center for Theoretical Physics（亚太理论物理中心）
机构由 AI 辅助整理，请以论文原文为准。
中文总结 AI 辅助
该论文从封闭量子系统的幺正演化出发，严格推导出局域子系统满足精确含时非厄米薛定谔方程，引入瞬时自能作为核心量，并通过基准对比揭示常规非厄米近似的局限性，为有效非厄米动力学提供了微观基础。
中文摘要 AI 辅助
从封闭量子系统的幺正演化出发，我们严格证明了全局波函数在任意局域子系统上的投影受一个精确的、含时的非厄米薛定谔方程支配。关键在于，该推导不依赖于诸如玻恩近似、马尔可夫近似或宽带极限等常规近似。核心量是瞬时自能，它是一个含时的、通常为非厄米的算符，编码了环境反作用，并与子系统哈密顿量一起构成投影动力学的精确含时局域生成元。通过将常规非厄米近似与该精确框架进行基准对比，我们系统地揭示了其局限性。这些结果为量子系统中有效非厄米动力学的涌现提供了严格的微观基础。
英文摘要
Starting from the unitary evolution of a closed quantum system, we rigorously demonstrate that the projection of the global wavefunction onto an arbitrary local subsystem is governed by an exact, time-dependent non-Hermitian Schrödinger equation. Crucially, the derivation does not rely on conventional approximations such as the Born approximation, the Markov approximation, or the wide-band limit. The central quantity is the \textit{instantaneous self-energy}, a time-dependent and generally non-Hermitian operator that encodes environmental backaction and, together with the subsystem Hamiltonian, forms the exact time-local generator of the projected dynamics. By benchmarking the conventional non-Hermitian approximation against this exact framework, we systematically expose its limitations. These results provide a rigorous microscopic foundation for the emergence of effective non-Hermitian dynamics in quantum systems.
