Green’s-function formalism for a condensed Bose gas consistent with infrared-divergent longitudinal susceptibility and Nepomnyashchii-Nepomnyashchii identity
Green’s-function formalism for a condensed Bose gas consistent with infrared-divergent longitudinal susceptibility and Nepomnyashchii-Nepomnyashchii identity
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与红外发散纵向磁化率和 Nepomnyashchii-Nepomnyashchii 恒等一致的凝聚玻色气体的格林函数形式主义
DOI：
10.1103/physreva.90.013603
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
and Y. Ohashi
中科院分区：
文献类型：
--
作者：
S. Watabe;and Y. Ohashi
我们提出了相互作用的玻色-爱因斯坦凝聚态 (BEC) 的格林函数形式，满足两个必需条件：(i) 相对于 BEC 阶数参数的红外发散纵向磁化率，以及 (ii) Nepomnyashchii-Nepomnyashchii 恒等式，说明在低能量和低动量极限下非对角线自能消失。这些条件不能用普通的平均场Bogoliubov理论、多体矩阵理论或带有顶点校正的随机相位近似来描述。在本文中，我们证明，当我们将多体校正分为奇异部分和非奇异部分，并将它们分别视为不同的自能校正时，可以满足这些所需条件。由此产生的格林函数可以被视为波波夫流体动力学理论在有限温度下区域的延伸。我们的结果将有助于构建一个一致的 BEC 理论，满足超出平均场水平的各种所需条件。
We present a Green's-function formalism for an interacting Bose-Einstein condensate (BEC) satisfying the two required conditions: (i) the infrared-divergent longitudinal susceptibility with respect to the BEC order parameter, and (ii) the Nepomnyashchii-Nepomnyashchii identity stating the vanishing off-diagonal self-energy in the low-energy and low-momentum limit. These conditions cannot be described by the ordinary mean-field Bogoliubov theory, the many-body-matrix theory, or the random-phase approximation with the vertex correction. In this paper, we show that these required conditions can be satisfied, when we divide many-body corrections into singular and nonsingular parts, and separately treat them as different self-energy corrections. The resulting Green's function may be viewed as an extension of the Popov's hydrodynamic theory to the region at finite temperatures. Our results would be useful in constructing a consistent theory of BECs satisfying various required conditions, beyond the mean-field level.