连续相空间中自旋的截断维格纳近似
Truncated Wigner approximation for spins in continuous phase space
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中文总结 AI 辅助
研究自旋的截断维格纳近似，利用维格纳 - 莫亚尔映射和规范自由度，推导运动方程并映射到随机微分方程，通过基准测试和应用展示其潜力，还可扩展到虚时间计算热态和基态，且能在路径积分方法内等效推导方程。
中文摘要 AI 辅助
我们回顾了自旋的截断维格纳近似（TWA），它是一种计算成本低的数值近似方法，用于描述相互作用和/或耗散的多体自旋系统。利用从希尔伯特空间到合适相空间的维格纳 - 莫亚尔映射，多体密度矩阵由一个 c 数分布即维格纳函数表示。利用连续相空间中的规范自由度可找到包括纠缠态在内的一大类自旋态的正维格纳函数。通过不同的对应规则集，我们推导了维格纳函数的运动方程，经控制近似可映射到随机微分方程，从而能低成本模拟期望值。利用量子回归定理的相空间类似物还可获得多时间关联和光谱。我们用一些可精确求解的相互作用、耗散自旋系统问题对自旋的 TWA 进行基准测试，并讨论其在集体过程中的应用，如光的超辐射发射。将 TWA 扩展到虚时间还提供了近似计算自旋哈密顿量热态和基态的工具。最后，我们表明只要耗散器中的算符乘积严格映射到弯曲相空间，TWA 随机方程可在路径积分方法内等效推导得出。
英文摘要
We review the truncated Wigner approximation (TWA) for spins as a computationally inexpensive numerical approximation method to describe interacting and / or dissipative many-body spin systems. Using the Wigner-Moyal mapping from Hilbert space to a suitable phase space, the many-body density matrix is represented by a c-number distribution, the Wigner function. The gauge freedom in continuous phase space can be exploited to find positive Wigner functions for a large class of spin states, including entangled ones. Employing different sets of correspondence rules, we derive equations of motion for the Wigner function, which, applying controlled approximations, can be mapped to stochastic differential equations. This allows a computationally inexpensive simulation of expectation values. Using a phase-space analog of the quantum regression theorem also multi-time correlations and spectra can be obtained. To illustrate the potential of the method, we benchmark the TWA for spins with some exactly solvable problems of interacting, dissipative spin systems, and then discuss its application to collective processes, such as the superradiant emission of light. Extending the TWA to imaginary time furthermore provides a tool to approximately calculate thermal and ground states of spin Hamiltonians. Finally, we show that the TWA stochastic equations can equivalently be derived within a path-integral approach, provided that the operator products in the dissipator are rigorously mapped onto the curved phase space.
