伊朗穆哈赫阿达比里大学Morteza NattaghNajafi小组的最新研究，提出了q变形费米子和玻色子的量子多体理论。这一研究成果于2025年2月20日发表在国际顶尖学术期刊《物理评论A》上。

研究团队提出了一个关于q变形费米子和玻色子的综合量子多体理论，提供了一个将粒子统计直接与有效相互作用强度联系起来的新框架。通过参数k和q的变形，这些粒子表现出介于传统玻色子和费米子系统之间的统计行为，使它们能够通过统计修改来模拟复杂的相互作用。

该研究团队发展了一个广义的维克定理和扩展的费曼图，为kq粒子量身定制，允许他们计算两种类型的格林函数。这些格林函数的显式表达式在直接和动量空间中都得到了推导，为费米子和玻色子系统的集体特性提供了关键的见解。

利用随机相位近似，研究人员估计了费米子气体()的介电函数，并分析了弗里德尔振荡、等离子激元激发和能量损失函数。他们的结果表明，有效相互作用的值被调整，从而得到一个非相互作用的极限，在这里弗里德尔振荡和等离子体振荡消失。等离子体频率和能量损失函数的最优值达到绝对最大值，有效相互作用改变了行为。

附：英文原文

Title: Quantum many-body theory for q-deformed fermions and bosons

Author: Habib Esmaili, Hosein Mohammadzadeh, Mehdi Biderang, Morteza NattaghNajafi

Issue&Volume: 2025/02/20

Abstract: We present a comprehensive quantum many-body theory for q-deformed fermions and bosons, offering a novel framework that relates particle statistics directly to effective interaction strength. Deformed by the parameters k and q, these particles exhibit statistical behaviors that interpolate between conventional bosonic and fermionic systems, enabling us to model complex interactions via statistical modifications. We develop a generalized Wick theorem and extended Feynman diagrammatics tailored to kq particles, allowing us to calculate two types of Green's functions. Explicit expressions for these Green's functions are derived in both direct and momentum spaces, providing key insights into the collective properties of -fermionic and bosonic systems. Using a random-phase approximation, we estimate the dielectric function for -fermion gas () and analyze the Friedel oscillations, the plasmon excitations, and the energy-loss function. Our results demonstrate that the effective interaction is tuned by the value of so that a noninteracting limit is obtained as , where the Friedel and the plasma oscillations disappear. An optimal value of , namely, , the plasma frequency, and the energy-loss function show an absolute maximum and the effective interaction changes behavior.

DOI: 10.1103/PhysRevA.111.022223

Source: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.111.022223