We describe an efficient numerical method for simulating the dynamics and steady states of collective spin systems in the presence of dephasing and decay. The method is based on the Schwinger boson representation of spin operators and uses an extension of the truncated Wigner approximation to map the exact open system dynamics onto stochastic differential equations for the corresponding phase space distribution. This approach is most effective in the limit of very large spin quantum numbers, where exact numerical simulations and other approximation methods are no longer applicable. We benchmark this numerical technique for known superradiant decay and spin-squeezing processes and illustrate its application for the simulation of non-equilibrium phase transitions in dissipative spin lattice models.

中文翻译：

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用于模拟自旋系统耗散多体动力学的相空间方法

我们描述了一种有效的数值方法，用于在存在相移和衰减的情况下模拟集体自旋系统的动力学和稳态。该方法基于自旋算子的Schwinger玻色子表示，并使用截断的Wigner逼近的扩展将确切的开放系统动力学映射到用于相应相空间分布的随机微分方程上。这种方法在非常大的自旋量子数限制中最为有效，在这种情况下，精确的数值模拟和其他近似方法不再适用。我们将该数值技术用于已知的超辐射衰减和自旋压缩过程，并说明了其在耗散自旋晶格模型中模拟非平衡相变的应用。