| Spectral Theorem of Many-Body Green＇s Functions When Complex Eigenvalues Appear |
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| 摘 要： | 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.
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| 关 键 词： | 多体格林函数 特征值 谱定理 傅立叶变换 相关函数 费米子 频率 虚部 |
| 收稿时间： | 2008-08-08 |
Spectral Theorem of Many-Body Green's Functions When Complex Eigenvalues Appear |
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| WANG Huai-Yu. Spectral Theorem of Many-Body Green's Functions When Complex Eigenvalues Appear[J]. Communications in Theoretical Physics, 2009, 51(5): 931-937 |
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| Authors: | WANG Huai-Yu |
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| Affiliation: | Department of Physics, Tsinghua University, Beijing 100084, China |
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| Abstract: | 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. |
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| Keywords: | spectral theorem many-body Green＇s functions correlation functions complex eigenvalues |
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