论文标题
精确$ \ MATHCAL {N} $ - 与Markovian开放量子系统的实验对之间的点函数映射
Exact $\mathcal{N}$-point function mapping between pairs of experiments with Markovian open quantum systems
论文作者
论文摘要
我们在$ \ Mathcal {n} $ - 点相关函数的两个不同实验的开放量子气体的函数之间制定了精确的时空映射。我们的形式主义扩展了封闭系统的量子场映射结果[Phys。 Rev. A \ TextBf {94}，043628（2016）]到具有Markovian属性的开放量子系统的一般情况。为此，我们考虑了一个开放的多体系统，该系统由玻色子的$ d $维量子气体组成，或者是在Born-Markov近似下与浴室相互作用的玻色子或费米子，并根据Lindblad Master方程在损失或收益方程中发展。在量子力学的图片上调用期望值的独立性，并使用描述气体动力学的量子场，我们得出当Lindblad发生器具有损失或增益时，系统在制度中的任何任意$ \ MATHCAL {N} $ - 系统点功能的Heisenberg演变。我们的封闭量子系统的量子场映射在Schrödinger图片中重写，然后通过相互关联到$ \ Mathcal {n} $ - 开放量子系统的点功能的两个不同的演变来扩展到打开量子系统。作为映射的具体示例，我们考虑了一个简单的耗散量子系统的平均场动力学，该系统由一维玻璃体凝结物组成，当两种情况下，当束振幅或腰部稳定且调节时，在两种情况下，都会在两种情况下都会被耗散电子束局部轰炸。
We formulate an exact spacetime mapping between the $\mathcal{N}$-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 \textbf{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 $\mathcal{N}$-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 Schrödinger picture and then extended to open quantum systems by relating onto each other two different evolutions of the $\mathcal{N}$-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.
