标题： 量子多体理论对于kq-变形粒子 显示英文标题

标题： Quantum Many-Body Theory for kq-Deformed Particles

摘要： 我们提出了一种全面的量子多体理论，用于kq变形粒子，提供了一个新颖的框架，将粒子统计直接与有效相互作用强度相关联。 由参数k和q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，使我们能够通过统计修改来模拟复杂的相互作用。 我们开发了一种广义的维克定理和针对kq粒子的扩展费曼图方法，使我们能够计算两种类型的格林函数。 这些格林函数在直接空间和动量空间中的显式表达式被推导出来，提供了对kq变形系统集体性质的关键见解。 使用随机相位近似（RPA），我们估计了q费米子气体的介电函数，并分析了弗里德尔振荡、等离子体激发和能量损耗函数。 我们的结果表明，有效相互作用由q的值调节，当q趋近于零时得到非相互作用极限，此时弗里德尔振荡以及等离子体振荡消失。 存在一个q的最优值，此时等离子体频率以及能量损耗函数显示出绝对最大值，有效相互作用的行为发生变化。 显示英文摘要

摘要： We present a comprehensive quantum many body theory for kq deformed particles, 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's theorem and extended Feynman diagrammatic tailored to kq-particles, allowing us to calculate two types of Green functions. Explicit expressions for these Green functions are derived in both direct and momentum spaces, providing key insights into the collective properties of kq-deformed systems. Using a random phase approximation (RPA), we estimate the dielectric function for q-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 q, so that a non interacting limit is obtained as q goes to zero, where the Friedel as well as the plasma oscillations disappear. There is an optimal value of q, the plasma frequency, as well as the energy loss function show an absolute maximum, and the effective interaction changes behavior.