O efeito Casimir em sistemas de N cavidades

Abstract

This work investigates the Casimir effect in multiple cavity systems using two complementary theoretical approaches. First, within the framework of integrable quantum field theories, we analyze the massive sine-Gordon model in (1+1) dimensions using the Boundary Thermodynamic Bethe Ansatz (BTBA) formalism. We propose and validate a generalization scheme for N identical plates, deriving a closed-form expression for the Casimir energy. The method’s consistency is explicitly verified by recovering known results in the conformal limit for n = 2 and the method is expanded by analyzing the case n = 3 plates. Second, we study a realistic model of stacked plasma sheets, developed within the Archimedes project, which aims to measure the weight of vacuum fluctuations. Using a finite-temperature canonical formalism and a transfer matrix approach for generating functions, we perform a detailed analysis of the asymptotic behavior for a large number of cavities N. Our main analytical contribution demonstrates the existence of a finite limit for the energy per cavity, limN→∞ EN/N = A, confirming numerical indications. We show that the total energy follows EN ≈ NE1 + Δ, where the coupling correction Δ saturates to a constant value, leading to an effectively additive behavior with a small asymptotic correction (∼ 3%). Furthermore, we provide a thermodynamic description of the multilayer system, introducing a layer chemical potential and deriving related quantities such as entropy and internal energy. The results bridge fundamental quantum field theory with potential experimental applications, offering new insights into the non-additivity and thermodynamic limit of Casimir forces in structured media.