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理论物理通讯：英文版

Spectral Theorem of Many-Body Green＇s Functions When Complex Eigenvalues Appear

Wang, Huaiyu

Published Jan 1, 2009• 0 citations
OpenAlex

Abstract

在这篇论文，一延长光谱当复杂特征值出现时，定理被给，它使一个能计算关联功能。到那么，有一个复杂参数的 Fourier 转变被利用。我们对待所有 Matsbara 频率，包括 Fermionic 和 Bosonic 频率，在相等的地位上。当复杂特征值出现时，一个系统的驱散不能简单地被归功于到格林函数的纯想象的部分，这被指出。因此，名字变化驱散定理的使用应该是小心的。

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在这篇论文，一延长光谱当复杂特征值出现时，定理被给，它使一个能计算关联功能。到那么，有一个复杂参数的 Fourier 转变被利用。我们对待所有 Matsbara 频率，包括 Fermionic 和 Bosonic 频率，在相等的地位上。当复杂特征值出现时，一个系统的驱散不能简单地被归功于到格林函数的纯想象的部分，这被指出。因此，名字变化驱散定理的使用应该是小心的。
In this paper, an extended spectral theorem is given, which enables one to calculate the correlation functions when complex eigenvalues appear. To do so, a Fourier transformation with a complex argument is utilized. We treat all the Matsbara frequencies, including Fermionic and Bosonic frequencies, on an equal footing. It is pointed out that when complex eigenvalues appear, the dissipation of a system cannot simply be ascribed to the pure imaginary part of the Green function. Therefore, the use of the name fluctuation-dissipation theorem should be careful.
In using the spectral theorem of many-body Green's function theory in order to relate correlations to commutator Green's functions, it is necessary in the standard procedure to consider the anti-commutator Green's functions as well whenever the matrix governing the equations of motion for the commutator Green's functions has zero eigenvalues. We show that a singular-value decomposition of this matrix allows one to reformulate the problem in terms of a smaller set of Green's functions with an associated matrix having no zero eigenvalues, thus eliminating the need for the anti-commutator functions. The procedure is quite general and easy to apply. It is illustrated for the field-induced reorientation of the magnetization of a ferromagnetic Heisenberg monolayer and it is expected to work for more complicated cases as well.