Resumo:
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.
