Stochastic field equations represent a powerful tool to describe the thermalstate of a trapped Bose gas. Often, such approaches are confronted with the oldproblem of an ultraviolet catastrophe, which demands a cutoff at high energies.In [arXiv:0809.1002, Phys. B 42, 081001 (2009)] we introduce a quantumstochastic field equation, avoiding the cutoff problem through a fully quantumapproach based on the Glauber-Sudarshan P-function. For a close link to actualexperimental setups the theory is formulated for a fixed particle number andthus based on the canonical ensemble. In this work the derivation and thenon-trivial numerical implementation of the equation is explained in detail. Wepresent applications for finite Bose gases trapped in a variety of potentialsand show results for ground state occupation numbers and their equilibriumfluctuations. Moreover, we investigate spatial coherence properties by studyingcorrelation functions of various orders.
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机译：随机场方程表示描述被捕集的玻色气体的热态的有力工具。通常，这种方法面临着紫外线灾难的旧问题，该问题需要在高能量下截止。[arXiv：0809.1002，Phys。 B 42，081001（2009）]中，我们引入了一个量子随机场方程，通过基于Glauber-Sudarshan P函数的完全量子方法避免了截止问题。为了与实际实验设置紧密联系，该理论被公式化为固定的粒子数，因此基于规范集合。在这项工作中，详细解释了方程的推导和非平凡的数值实现。我们介绍了被困在各种电位中的有限玻色气体的应用，并给出了基态占有数及其平衡涨落的结果。此外，我们通过研究各种阶次的相关函数来研究空间相干性。
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