AI 中文总结
研究驱动耗散自旋截断维格纳近似，利用连续SU(2)相空间为相互作用开放自旋 - 1/2系统建立路径积分公式，通过正确映射算符乘积到弯曲相空间得出随机方程，为TWA提供统一场论基础及扩展起点。
AI 中文摘要
相空间方法如截断维格纳近似（TWA）为开放量子多体系统动力学的近似模拟提供了一个有效的半经典框架。对于玻色子系统，TWA等同于在所谓量子涨落二阶截断的凯尔迪什路径积分公式。本文为相互作用的开放自旋 - 1/2系统建立了相应的路径积分公式，表明对耗散的一致处理需要将算符乘积正确映射到弯曲的自旋相空间，得到与连续TWA公式一致的随机方程，再现单个耗散自旋的精确动力学，为TWA提供了统一的场论基础。
英文摘要
Phase-space approaches such as the truncated Wigner approximation (TWA) provide an efficient semiclassical framework for performing approximate simulations of the dynamics of open quantum many-body systems outside the reach of exact numerical methods but beyond the mean-field level. For bosonic systems, TWA is known to be equivalent to a Keldysh path-integral formulation truncated at second order in the so-called quantum fluctuations. This semiclassical approach provides an alternative transparent route towards approximate stochastic equations of motion, which can be efficiently solved. Here we establish the corresponding path-integral formulation for interacting open spin-$1/2$ systems using the continuous $\mathrm{SU}(2)$ phase space. We show, in particular, that a consistent treatment of dissipation requires correctly mapping operator products onto the curved spin phase space, leading to stochastic equations that coincide with those obtained from the continuous TWA formulation and thus reproduce the exact dynamics of a single dissipative spin. Our results provide a unified field-theoretic foundation for the TWA to dissipative spin dynamics and offer a systematic starting point for extensions beyond the semiclassical approximation.
