The classical field approximation is widely used to better understand the predictions of ultralight dark matter. Here, we use the truncated Wigner approximation method to test the classical field approximation of ultralight dark matter. This method approximates a quantum state as an ensemble of independently evolving realizations drawn from its Wigner function. The method is highly parallelizable and allows the direct simulation of quantum corrections and decoherence times in systems many times larger than have been previously studied in reference to ultralight dark matter. Our study involves simulation of systems in 1, 2, and 3 spatial dimensions. We simulate three systems, the condensation of a Gaussian random field in three spatial dimensions, a stable collapsed object in three spatial dimensions, and the merging of two stable objects in two spatial dimensions. We study the quantum corrections to the classical field theory in each case. We find that quantum corrections grow exponentially during nonlinear growth with the timescale being approximately equal to the system dynamical time. In stable systems the corrections grow quadratically. We also find that the primary effect of quantum corrections is to reduce the amplitude of fluctuations on the de Broglie scale in the spatial density. Finally, we find that the timescale associated with decoherence due to gravitational coupling to baryonic matter is at least as fast as the quantum corrections due to gravitational interactions. These results are consistent with the predictions of the classical field theory being accurate.

中文翻译：

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超轻暗物质的经典场近似：量子断裂时间、校正和退相干

经典场近似被广泛用于更好地理解超轻暗物质的预测。在这里，我们使用截断维格纳近似方法来测试超轻暗物质的经典场近似。该方法将量子态近似为从其维格纳函数得出的独立演化实现的集合。该方法具有高度可并行性，并且允许在比之前参考超轻暗物质研究的系统大许多倍的系统中直接模拟量子校正和退相干时间。我们的研究涉及 1、2 和 3 空间维度的系统模拟。我们模拟了三个系统，三个空间维度中高斯随机场的凝聚，三个空间维度中的稳定塌缩物体，以及两个空间维度中两个稳定物体的合并。我们研究每种情况下对经典场论的量子修正。我们发现，在非线性增长过程中，量子校正呈指数增长，时间尺度约等于系统动态时间。在稳定系统中，修正量呈二次方增长。我们还发现，量子校正的主要作用是减少空间密度中德布罗意尺度的波动幅度。最后，我们发现由于与重子物质的引力耦合而导致的退相干相关的时间尺度至少与由于引力相互作用而产生的量子校正一样快。这些结果与经典场论的准确预测是一致的。