We consider the homogeneous mean-field Bose gas at temperatures proportional to the critical temperature of its Bose-Einstein condensation phase transition. We prove a trace norm approximation for the grand canonical Gibbs state in terms of a reference state, which is given by a convex combination of products of coherent states and Gibbs states associated with certain temperature-dependent Bogoliubov Hamiltonians. The convex combination is expressed as an integral over a Gibbs distribution of a one-mode $Φ^4$-theory describing the condensate. This result justifies an analogue of Lee and Yang's extension of Bogoliubov theory to positive temperatures, and it allows us to derive various limiting distributions for the number of particles in the condensate, as well as precise formulas for the one- and two-particle density matrices of the Gibbs state. Key ingredients of our proof, which are of independent interest, include two novel abstract correlation inequalities. The proof of one of them is based on an application of an infinite-dimensional version of Stahl's theorem.
Simulating Thermal Properties of Bose-Hubbard Models on a Quantum Computer
Bocconi University（博科尼大学）；Inria, Télécom Paris – LTCI, Institut Polytechnique de Paris（法国国家信息与自动化研究所，巴黎电信学院-通信与图像处理实验室，巴黎理工学院）；Institute for Quantum Information, RWTH Aachen University（亚琛工业大学量子信息研究所）；Inria, ENS de Lyon, Université Claude Bernard Lyon 1, LIP（法国国家信息与自动化研究所，里昂高等师范学院，克莱伯贝尔·里昂第一大学，计算与图像实验室）
The equilibrium states for a model with two kinds of Bose condensation
本文研究了由Bru和Zagrebnov定义的玻色气体模型的平衡吉布斯态，该模型具有两个玻色凝聚型的相变。这两种相变对应于两种不同的机制，通过这两种机制可以发生这些冷凝。第一（非常规）玻色凝聚介导的零模相互作用项的哈密顿量。第二个是由于饱和的过渡非常类似于传统的玻色-爱因斯坦（BE）凝聚在理想玻色气体。由于非零模式中的排斥相互作用，该模型表现出广义的III型，即，非广泛BE缩合。我们的主要结果是，在理想玻色气体中，常规凝聚伴随着正则和巨正则系综的强等价性的损失，而非常规的，由于相互作用，不打破系综的等价性。有趣的是，（广义）凝聚的类型，I、II或III（用van den Berg、Lewis和Pule的术语），对系综的等价性没有影响。通过计算对应平衡吉布斯态的正则对易关系（CCR）的循环表示的生成泛函，证明了这些结果。
Quasicrystalline Gibbs states in 4-dimensional lattice-gas models with finite-range interactions
University of Warsaw, Institute of Applied Mathematics and Mechanics（华沙大学应用数学和力学研究所）；Department of Mathematics & Center for Advanced Mathematical Sciences, American University of Beirut（贝鲁特美国大学数学系与高级数学科学中心）
