Strong connection between single-particle and density excitations in Bose-Einstein condensates
Strong connection between single-particle and density excitations in Bose-Einstein condensates
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玻色-爱因斯坦凝聚中单粒子和密度激发之间的紧密联系
DOI：
10.1088/1367-2630/abb2b6
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发表时间：
2020
影响因子：
3.3
通讯作者：
Shohei Watabe
中科院分区：
文献类型：
--
作者：
八田振一郎;綾遥奈;奥山弘;有賀哲也;Shohei Watabe
单粒子激发和集体激发之间的强联系是玻色-爱因斯坦凝聚（BECs）的特征之一。我们从理论上讨论了BECs的单粒子和密度激发，重点讨论了由Gavoret和nozi<e:1>提出的一体和二体格林函数的确切性质。我们还利用非零温度下的多体近似理论研究了这些激发。首先，我们回顾了Gavoret和nozi<e:1>的早期研究，涉及Nepomnyashchii和Nepomnyashchii在矩阵形式主义表示方面给出的后续结果。这种矩阵形式是对BECs单粒子格林函数的Nambu表示的一种扩展，可以有效地讨论密度和电流响应函数。我们精确地描述了相关函数和顶点函数的低能性质，并讨论了T= 0低能和低动量极限下单粒子激发和密度激发谱的对应关系。在推导出单粒子格林函数和双粒子格林函数的精确低能结构后，我们利用矩阵形式描述了非零温度下的单粒子格林函数和密度响应函数，建立了多体近似理论。我们展示了单粒子谱函数和密度响应函数的峰值是如何随温度升高而变化的。多体效应对单粒子谱函数和密度响应函数的影响被包含在随机相位近似中，其中卫星结构由于超平均场效应而出现。对最近的理论也提出了批评，这些理论对BEC的传统智慧提出了质疑：在低能量和低动量状态下，单粒子激发和集体激发之间的色散关系是等效的。
Strong connection between the single-particle excitation and the collective excitation stands out as one of the features of Bose–Einstein condensates (BECs). We discuss theoretically these single-particle and density excitations of BECs focusing on the exact properties of the one-body and two-body Green's functions developed by Gavoret and Nozières. We also investigate these excitations by using the many-body approximation theory at nonzero temperatures. First, we revisited the earlier study presented by Gavoret and Nozières, involving the subsequent results given by Nepomnyashchii and Nepomnyashchii, in terms of the matrix formalism representation. This matrix formalism is an extension of the Nambu representation for the single-particle Green's function of BECs to discuss the density and current response functions efficiently. We describe the exact low-energy properties of the correlation functions and the vertex functions, and discuss the correspondence of the spectra between the single-particle excitation and the density excitation in the low-energy and low-momentum limits at T= 0. After deriving the exact low-energy structures of the one-body and two-body Green's functions, we develop a many-body approximation theory of BECs with making the use of the matrix formalism for describing the single-particle Green's function and the density response function at nonzero temperatures. We show how the peaks of the single-particle spectral function and the density response function behave with an increasing temperature. Many-body effect on the single-particle spectral function and the density response function is included within a random phase approximation, where satellite structures emerge because of beyond-mean-field effects. Criticisms are also made on recent theories casting doubt upon the conventional wisdom of the BEC: the equivalence of the dispersion relations between the single-particle excitation and the collective excitation in the low-energy and low-momentum regime.