双势阱中具有平衡增益和损耗的玻色-爱因斯坦凝聚体表现出PT对称态。正如Kreibich等人[Phys. Rev. A 87，051601（R）（2013）]所提出的，在平均场极限下，该系统的动力学行为，特别是PT对称态的动力学行为，可以通过将其嵌入具有时间依赖参数的埃尔米特四阱系统来模拟。在本文中，我们超越了平均场近似，并研究在这个系统中的多体效应，这是在最低阶描述的单粒子密度矩阵。单粒子密度矩阵中的PT对称性条件不能用纯初态完全满足。在这里，我们表明，它是数学上可能实现精确的PT对称性在四阱多体系统的意义上的单粒子密度矩阵的动力学行为。与以前的工作相比，为了这个目的，我们使用混合初始状态满足一定的约束条件，并使用它们来计算动态。
英文摘要：
Bose-Einstein condensates with balanced gain and loss in a double-well potential have been shown to exhibit PT-symmetric states. As proposed by Kreibich et al [Phys. Rev. A 87, 051601(R) (2013)], in the mean-field limit the dynamical behaviour of this system, especially that of the PT-symmetric states, can be simulated by embedding it into a Hermitian four-well system with time-dependent parameters. In this paper we go beyond the mean-field approximation and investigate many-body effects in this system, which are in lowest order described by the single-particle density matrix. The conditions for PT symmetry in the single-particle density matrix cannot be completely fulfilled by using pure initial states. Here we show that it is mathematically possible to achieve exact PT symmetry in the four-well many-body system in the sense of the dynamical behaviour of the single-particle density matrix. In contrast to previous work, for this purpose, we use mixed initial states fulfilling certain constraints and use them to calculate the dynamics.
Polynomial-time certification of fidelity for many-body mixed states and mixed-state universality classes
Max Planck Institute of Quantum Optics（马克斯·普朗克量子光学研究所）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）；Perimeter Institute for Theoretical Physics（理论物理前沿研究所）
Analytical solution of the Schrödinger equation with $1/r^3$ and attractive $1/r^2$ potentials: Universal three-body parameter of mixed-dimensional Efimov states
University of Electro-Communications（电气通信大学）；Tohoku University（东北大学）
Open Quantum Systems as Regular Holonomic $\mathcal{D}$-Modules: The Mixed Hodge Structure of Spectral Singularities
State Key Laboratory for Precision Spectroscopy, ECNU, Shanghai（精密光谱学国家重点实验室，华东师范大学）；Dept. of Chemistry/Physics, University of California,Irvine（加州大学欧文分校化学/物理系）；QuMorpheus Initiative（QuMorpheus倡议）
