标题： 有限温度下的相互玻色子：博戈柳波夫如何拜访黑洞并安全返回 显示英文标题

标题： Interacting Bosons at Finite Temperature: How Bogolubov Visited a Black Hole and Came Home Again

摘要： 弱相互作用玻色气体热平衡态的结构是当前的研究热点。 我们用两种方法计算该态的密度矩阵。 就得到简单且明确的答案而言，最有效的方法是在量子统计力学的传统框架内构造生成函数。 另一种方法，或许更有趣，是将热态构造成一个具有两倍自由度的人工系统的矢量态。 众所周知，在黑洞的量子热力学中，这种构造有一个实际的物理实现，其中增加的自由度对应于克鲁斯卡尔流形的第二层，而热态矢量对应于乌尔哈或哈特尔-哈金类型的态。 这项工作的不寻常之处在于，用来构造热态的博戈柳博夫变换以一种相当对称的方式与博戈柳博夫原始的同类型变换结合在一起，后者用于以线性近似方式实现非理想气体的相互作用。 除了提供密度矩阵外，这种方法还使得能够直接利用加倍系统中的热态矢量有效地计算某些期望值。 显示英文摘要

摘要： The structure of the thermal equilibrium state of a weakly interacting Bose gas is of current interest. We calculate the density matrix of that state in two ways. The most effective method, in terms of yielding a simple, explicit answer, is to construct a generating function within the traditional framework of quantum statistical mechanics. The alternative method, arguably more interesting, is to construct the thermal state as a vector state in an artificial system with twice as many degrees of freedom. It is well known that this construction has an actual physical realization in the quantum thermodynamics of black holes, where the added degrees of freedom correspond to the second sheet of the Kruskal manifold and the thermal vector state is a state of the Unruh or the Hartle-Hawking type. What is unusual about the present work is that the Bogolubov transformation used to construct the thermal state combines in a rather symmetrical way with Bogolubov's original transformation of the same form, used to implement the interaction of the nonideal gas in linear approximation. In addition to providing a density matrix, the method makes it possible to calculate efficiently certain expectation values directly in terms of the thermal vector state of the doubled system.