Aspectos do vácuo escalar em coordenadas generalizadas: estudo do efeito Casimir e efeito Unruh - Lima, Augusto Plácido Cavalcante Melo de (2020)
The present work proposes an approach for two discussions concerning the nature of the quantum vacuum in the perspective of generalized coordinates and curved space-times. For simplicity, we use a real massless scalar field for the models. The first consists of the discussion of the Casimir effect in a weak gravitational field, a problem that has been approached before in the literature by other authors. Using both the canonical and the functional formalism we demonstrate that the Casimir energy obtained for Dirichlet boundary conditions in paralell plates has no gravitational correction to order of [M/R]² , taken as the first non-trivial order in previous works. We show that this result is valid for a wider class of geometries, indicating a discrepancy with these previous results from other authors. The second discussion approaches the distinguishablity of the effects of thermalization of the vacuum in the frame of an accelerated observer, the Unruh effect, and the influence of a common thermal bath on a Unruh-Dewitt detector. Using the formalism of open quantum systems, specifically a markovian approximation of the master equation for the detector’s state density, we annalyze the effects of temperature and acceleration in the case where both effects are simultaneously present. We implement an simplified numerical approach to obtain the assyntotical state density for one accelerated particle and entanglement formation for two particles. The obtained curves indicate a small assimmetry in the dependencies of the two quantities with the background temperature and the acceleration.