发表机构
HSE University; G.A. Krestov Institute of Solution Chemistry of the Russian Academy of Sciences（高等经济学院; 俄罗斯科学院 G.A.克雷斯托夫溶液化学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出有限温度场论描述量子玻尔兹曼等离子体对卡西米尔力的屏蔽，揭示经典极限的德拜屏蔽及量子修正，并建立与林哈德响应和朗道抗磁性的对应。
AI 中文摘要
我们发展了一个有限温度场论描述，用于研究两个完美导体边界之间的卡西米尔相互作用，其间间隙填充了嵌入均匀介电背景中的双组分量子玻尔兹曼等离子体。带电粒子的量子运动由虚时世界线表示，而电磁场在高斯近似下处理。由此得到的配分函数包含不同的纵向和横向响应贡献，以及一个没有经典对应物的额外量子诱导源项。在经典极限下，该理论简化为通常的卡西米尔屏蔽图像：静态纵向模式被德拜屏蔽，而横向电磁扇区不受经典可移动电荷的影响。有限热德布罗意波长修改了非零马苏巴纳响应，并产生了力的主要量子修正。在静态长波长极限下，纵向介电函数通过主要量子修正具有与简并电子气的林哈德响应相同的展开结构，在对应关系 $k_{TF}\leftrightarrow\kappa_D$ 和 $k_F\leftrightarrow\lambda_{dB}^{-1}$ 下，而静态横向响应再现了主要的高温朗道轨道抗磁磁化率。
英文摘要
We develop a finite-temperature field-theoretical description of the Casimir interaction between two perfectly conducting boundaries with the intervening gap filled by a two-component quantum Boltzmann plasma embedded in a homogeneous dielectric background. The quantum motion of the charged particles is represented by imaginary-time worldlines, while the electromagnetic field is treated in the Gaussian approximation. The resulting partition function contains distinct longitudinal and transverse response contributions and an additional quantum-induced source term with no classical counterpart. In the classical limit the theory reduces to the usual Casimir-screening picture: the static longitudinal mode is Debye screened, whereas the transverse electromagnetic sector is unaffected by classical mobile charges. Finite thermal de Broglie wavelengths modify the nonzero Matsubara response and produce the leading quantum correction to the force. In the static long-wavelength limit, the longitudinal dielectric function has, through the leading quantum correction, the same expansion structure as the Lindhard response of a degenerate electron gas under the correspondence $k_{TF}\leftrightarrowκ_D$ and $k_F\leftrightarrowλ_{dB}^{-1}$, while the static transverse response reproduces the leading high-temperature Landau orbital diamagnetic susceptibility.
CommentsSubmitted to The Journal of Chemical Physics
