We formulate an exact spacetime mapping between the $𝒩$-point correlation functions of two different experiments with open quantum gases. Our formalism extends a quantum-field mapping result for closed systems [Phys. Rev. A 94, 043628 (2016)] to the general case of open quantum systems with Markovian property. For this, we consider an open many-body system consisting of a $D$-dimensional quantum gas of bosons or fermions that interacts with a bath under Born-Markov approximation and evolves according to a Lindblad master equation in a regime of loss or gain. Invoking the independence of expectation values on pictures of quantum mechanics and using the quantum fields that describe the gas dynamics, we derive the Heisenberg evolution of any arbitrary $𝒩$-point function of the system in the regime when the Lindblad generators feature a loss or a gain. Our quantum field mapping for closed quantum systems is rewritten in the Schr"odinger picture and then extended to open quantum systems by relating onto each other two different evolutions of the $𝒩$-point functions of the open quantum system. As a concrete example of the mapping, we consider the mean-field dynamics of a simple dissipative quantum system that consists of a one-dimensional Bose-Einstein condensate being locally bombarded by a dissipating beam of electrons in both cases when the beam amplitude or the waist is steady and modulated.

中文翻译：

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使用马尔可夫开放量子系统的实验对之间的精确点函数映射

我们在两者之间建立了精确的时空映射 $𝒩$开放量子气体的两个不同实验的定点相关函数。我们的形式主义扩展了封闭系统的量子场映射结果。Rev. A 94，043628（2016）]对具有马尔可夫性质的开放量子系统的一般情况。为此，我们考虑一个开放的多体系统，其中包括$d$玻色子或费米子的二维量子气体，在Born-Markov近似下与浴相互作用，并根据Lindblad主方程在损耗或增益状态下演化。在量子力学的图片上调用期望值的独立性，并使用描述气体动力学的量子场，我们可以推导出任意任意的海森堡演化$𝒩$Lindblad发电机具有损耗或增益特性时，系统在系统中的定点功能。我们针对封闭量子系统的量子场映射在Schr“ odinger图片中进行了重写，然后通过彼此关联两个不同的量子演化而扩展到开放量子系统。$𝒩$量子系统的点函数。作为映射的一个具体示例，我们考虑一个简单的耗散量子系统的平均场动力学，该系统由一维Bose-Einstein凝聚物组成，在两种情况下，当电子束的振幅或电子束的束缚力都受到电子的耗散束轰击时腰部稳定而调节。