论文标题
Bose-Einstein冷凝水中的单粒子和密度激发之间的牢固联系
Strong connection between single-particle and density excitations in Bose-Einstein condensates
论文作者
论文摘要
单粒子和集体激发之间的牢固联系是Bose-Einstein冷凝物（BEC）的特征之一。从理论上讲，我们讨论了BEC的这些激励，重点介绍了Gavoret和Nozières开发的一体和两体绿色功能的确切特性。我们还通过在非零温度下使用多体近似理论来研究这些激发。首先，我们重新审视了Gavoret和Nozières提出的早期研究，涉及Nepomnyashchii和Nepomnyashchii的后续结果，就矩阵形式主义表示而言。这种形式主义是单粒子绿色的BEC功能的NAMBU表示的扩展，以有效地讨论密度和当前响应功能。我们描述了相关函数和顶点函数的确切低能特性，并讨论了在$ t = 0 $的低能和低巨型限制中单粒子和密度激发之间光谱的对应关系。在得出一体和两体绿色功能的确切低能结构之后，我们使用矩阵形式主义来开发BEC的多体近似理论，用于描述非零温度下的单粒子绿色功能和密度响应函数。我们展示了单粒子光谱函数的峰和密度响应函数的表现，温度的升高。多体对单粒子光谱函数和密度响应函数的影响包括在随机相位近似中，其中卫星结构由于超出均值效果而出现。还对最近的理论提出了批评，以对BEC的传统观念产生怀疑：在低能量和低摩托明政权中，单粒子之间的分散关系与集体激发之间的分散关系等效。
Strong connection between the single-particle and collective excitations stands out as one of the features of Bose-Einstein condensates (BECs). We discuss theoretically these 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 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 and density excitations 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 using 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 and collective excitations in the low-energy and low-momentum regime.
