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arXiv 1908.11202quant-phmath-phmath.MP
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低密度极限下与量子气体相互作用系统的量子主方程及半经典碰撞模型

Quantum master equations for a system interacting with quantum gas in the low density limit and for the semiclassical collision model

S. N. Filippov, G. N. Semin, A. N. Pechen

备注：
11 pages, 4 figures, published version with stronger results in the high-temperature limit
发表信息：
Phys. Rev. A 101, 012114 (2020)
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摘要：

与稀气体相互作用的量子系统经历不可逆动力学。相应的主方程可以用两种不同的方法导出：低密度极限下的全量子描述和半经典碰撞模型，其中气体粒子的运动是经典的，而它们的内部自由度是量子的。这两种方法在文献中得到了广泛的研究，但它们的预测没有进行比较。这主要是因为低密度极限是为了数学物理的目的而被广泛研究的，而碰撞模型基本上是为了量子信息的任务而开发的，例如开放量子动力学的易处理的描述。在这里，我们开发和第一次比较这两种方法的自旋系统与气体的自旋粒子相互作用。使用一些近似，我们明确地找到相应的主方程，包括兰姆位移和耗散。证明了快粒子玻恩近似中的低密度极限与频闪近似中的半经典碰撞模型是等价的。我们发现，这两种方法给出完全相同的主方程，如果气体温度足够高。这允许在低密度极限中交替使用复杂的计算和在碰撞模型中交替使用相当简单的计算。

英文摘要：

A quantum system interacting with a dilute gas experiences irreversible dynamics. The corresponding master equation can be derived within two different approaches: The fully quantum description in the low-density limit and the semiclassical collision model, where the motion of gas particles is classical whereas their internal degrees of freedom are quantum. The two approaches have been extensively studied in the literature, but their predictions have not been compared. This is mainly due to the fact that the low-density limit is extensively studied for mathematical physics purposes, whereas the collision models have been essentially developed for quantum information tasks such as a tractable description of the open quantum dynamics. Here we develop and for the first time compare both approaches for a spin system interacting with a gas of spin particles. Using some approximations, we explicitly find the corresponding master equations including the Lamb shifts and the dissipators. The low density limit in the Born approximation for fast particles is shown to be equivalent to the semiclassical collision model in the stroboscopic approximation. We reveal that both approaches give exactly the same master equation if the gas temperature is high enough. This allows to interchangeably use complicated calculations in the low density limit and rather simple calculations in the collision model.

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