薛定谔绘景与海森堡绘景的幺正等价性在非线性量子力学中仍然成立
Unitary equivalence of Schrödinger and Heisenberg pictures survives in nonlinear quantum mechanics
- Wigner Research Center for Physics（维格纳物理研究中心）
- Eötvös Loránd University（罗兰大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文证明在非线性量子力学中，当哈密顿量依赖于瞬时期望值时，薛定谔绘景与海森堡绘景的幺正等价性仍成立，尽管交织算子依赖初始状态，但物理预言一致。
AI中文摘要：
薛定谔绘景与海森堡绘景的等价性常被认为在非线性量子力学中因缺乏与状态无关的幺正传播子而失效。我们证明，对于通过瞬时期望值依赖于状态的哈密顿量，这种等价性得以保留。尽管幺正交织算子依赖于初始状态，它仍然是良定义的，并确保两种绘景给出相同的物理预言。我们通过解析可解的示例加以说明，包括非线性自旋进动和平均场谐振力，以及在具有平均场耦合的局域场论中。
英文摘要：
The equivalence of Schrödinger and Heisenberg pictures is often thought to break down in nonlinear quantum mechanics due to the absence of a state-independent unitary propagator. We show that for Hamiltonians depending on the state through instantaneous expectation values, the equivalence is preserved. While the unitary intertwiner becomes initial-state dependent, it remains well-defined and ensures identical physical predictions in both pictures. We illustrate this with the analytically solvable examples of a nonlinear spin precession and a mean-field harmonic force, as well as in local field theory with mean-field coupling.
