量子统一统计多体理论基础：格林函数与线性响应理论
Foundations of Many-Body Theory of Quantum Unified Statistics: Green functions and Linear Response Theory
- University of Mohaghegh Ardabili（莫哈杰·阿尔达比勒大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文为量子统一统计（quon）粒子系统建立多体理论框架，通过广义Wick定理和格林函数形式体系，结合随机相位近似推导介电函数，发现反常等离激元模式，并分析无限统计对集体行为与屏蔽性质的定性影响。
AI中文摘要：
我们为服从量子统一统计（即quons）的粒子系统发展了一套全面的多体理论。在探索了该系统的Fock空间性质后，我们系统地阐述了S矩阵展开和广义Wick定理。我们在零温和有限温度下构建了自洽的格林函数形式体系，并辅以适用于无限统计算子代数的广义Wick定理。在此框架内，我们为相互作用的quon系统建立了图解规则。采用随机相位近似，我们推导了介电函数，并揭示了在传统玻色或费米系统中没有直接对应物的反常等离激元模式的出现。我们进一步分析了基态能量、能量损失函数、广义托马斯-费米屏蔽波矢和弗里德尔振荡，阐明了无限统计如何定性改变集体行为和屏蔽性质。
英文摘要：
We develop a comprehensive many-body theory for systems of particles obeying quantum unified statistics, or quons. After exploring the properties of the Fock space of this system, we formulate a systematic S-matrix expansion and a generalized Wick's theorem. A consistent Green-function formalism is constructed at both zero and finite temperatures, accompanied by a generalized Wick's theorem appropriate for infinite-statistics operator algebras. Within this framework, we establish diagrammatic rules for interacting quon systems. Employing the random phase approximation, we derive the dielectric function and reveal the emergence of anomalous plasmon modes that have no direct counterpart in conventional Bose or Fermi systems. We further analyze the ground-state energy, energy-loss function, generalized Thomas-Fermi screening wave vectors, and Friedel oscillations, elucidating how infinite statistics qualitatively modifies collective behavior and screening properties.
