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arXiv 2412.20751cond-mat.quant-gasnucl-th
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有限温度下超流费米子的响应

Response of superfluid fermions at finite temperature

Western Michigan University(西密歇根大学)

Sumit Bhattacharjee, Elena Litvinova

AI总结:

本文提出了一种有限温度下超流费米子响应的微观理论,通过博格利亚夫变换引入超流性,并通过因子化形式简化多体问题,同时考虑准粒子-振动耦合效应。

摘要:

一个一致的有限温度微观理论被提出,用于描述强耦合超流费米子系统的响应。我们从一般的多体哈密顿量出发,考虑真空(裸)两费米子相互作用,推导出热平均的两时间两费米子相关函数的运动方程(EOM),该方程决定了所研究系统的谱。超流性通过费米子场算符的博格利亚夫变换引入,整个形式化在博格利亚夫准粒子基底下进行,保持两费米子EOM的完整4x4块矩阵结构。讨论了由此产生的EOM的完全相关静态和动态相互作用核。特别关注后者核,将其推进到因子化形式,使许多体问题能够进行最小截断,同时保持重要涌现集体性效应和映射到准粒子-振动耦合(qPVC)。如同零温度和非超流情况,qPVC可以与一个新的序参量,qPVC顶点相关联。在热超流理论中,后者顶点以及动态核的组成部分获得扩展形式,包括热未阻断的跃迁振幅。

英文摘要:

A consistent finite-temperature microscopic theory for the response of strongly coupled superfluid fermionic systems is formulated. We start from the general many-body Hamiltonian with the vacuum (bare) two-fermion interaction and derive the equation of motion (EOM) for the thermally averaged two-time two-fermion correlation function, which determines the spectrum of the system under study. The superfluidity is introduced via the Bogoliubov transformation of the fermionic field operators, and the entire formalism is carried out in the basis of Bogoliubov's quasiparticles, keeping the complete 4x4 block matrix structure of the two-fermion EOM. Fully correlated static and dynamical interaction kernels of the resulting EOM are discussed. A special focus is then placed on the latter kernel, which is advanced to a factorized form, enabling a minimal truncation of the many-body problem while keeping important effects of emergent collectivity and mapping to the quasiparticle-vibration coupling (qPVC). As in the zero-temperature and non-superfluid cases, the qPVC can be associated with a new order parameter, qPVC vertex. In the thermal superfluid theory, the latter vertex, as well as the components of the dynamical kernel, acquire an extended form including thermally unblocked transition amplitudes.

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