发表机构
Universidade Federal da Paraíba（帕拉伊巴联邦大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究平行板间大质量标量场在位置依赖有效质量下的卡西米尔效应，通过求解克莱因 - 戈登方程获精确模式，经量子化和正则化评估真空能量，结果表明两种贡献在不同区域有不同表现，建立了与量子真空现象联系并提供新框架。
AI 中文摘要
我们研究了在存在位置依赖有效质量（一种将标量背景与标量场耦合的机制）的情况下，限制在两个完全反射平行板之间的大质量实标量场的卡西米尔效应。通过求解相应的克莱因 - 戈登方程获得精确的正常模式，得到了一个横向能谱，尽管没有外部磁场，但它呈现出类似朗道的特征结构。对场进行量子化后，通过广义zeta函数正则化和适当的重整化程序评估真空能量。重整化后的真空能量自然地分为类似朗道的贡献和由有效质量的空间依赖性引起的附加项。我们通过解析和数值方法表明，在强耦合区域，这两种贡献都被指数抑制。在相反的极限情况下，类似朗道的贡献平滑地再现了限制在平行板之间的大质量标量场的标准真空能量，而附加贡献由于精确谱的有效域受限而变得奇异。除了在这个奇异极限附近，真空能量由类似朗道的部分主导。我们的结果建立了位置依赖有效质量与边界诱导量子真空现象之间的直接联系，为研究空间非均匀相对论系统中的卡西米尔效应提供了一个新的精确可解框架。
英文摘要
We investigate the Casimir effect for a massive real scalar field confined between two perfectly reflecting parallel plates in the presence of a position-dependent effective mass, a mechanism for coupling a scalar background to a scalar field. Exact normal modes are obtained by solving the corresponding Klein-Gordon equation, leading to a transverse energy spectrum that exhibits a characteristic Landau-like structure despite the absence of an external magnetic field. Upon quantization of the field, the vacuum energy is evaluated by means of generalized zeta-function regularization together with an appropriate renormalization procedure. The renormalized vacuum energy naturally separates into a Landau-like contribution and an additional term induced by the spatial dependence of the effective mass. We show analytically and numerically that both contributions are exponentially suppressed in the strong-coupling regime. In the opposite limit, the Landau-like contribution smoothly reproduces the standard vacuum energy for a massive scalar field confined between parallel plates, whereas the additional contribution becomes singular owing to the restricted domain of validity of the exact spectrum. Except in the vicinity of this singular limit, the vacuum energy is shown to be dominated by the Landau-like sector. Our results establish a direct connection between position-dependent effective masses and boundary-induced quantum vacuum phenomena, providing a new exactly solvable framework for the investigation of Casimir effects in spatially inhomogeneous relativistic systems.
Comments13 pages, 3 figures, accepted for publication in Physics Letters B
