Casimir Effect in systems in and out of Equilibrium

Abstract: This thesis consists on two separate parts. In the first part, we discuss about the nature of the Casimir effect as the response of a fluctuant medium to the breakdown of the translation symmetry because the presence of intrusions in that medium. To do so, we present a dynamical approximation of Casimir effect, which generalizes Casimir effect studies to out of equilibrium steady states. The equilibrium known case is recovered as a particular case, including the case of electromagnetic (EM) Casimir effect generated because of quantum fluctuations. This formalism also allows us to define (and calculate) the variance of Casimir forces. In the second part of this thesis, by the use of a Multiscattering formalism, we study the nature of the multibody Casimir effect. We demonstrate that the Casimir force and energy between two spheres in presence of a plate (perfect metal objects all of them) is non-monotonous with the distance between spheres and between sphere and plate. We derive the Pairwise Summation Approximation (PSA) of the EM field from this multiscattering formalism for generalized dielectrics, including magnetic responses and Topological Insulators as an example of magnetoelectric couplings. We also study the nonmonotonous behavior of the entropy with the temperature for a system of two perfect metal spheres and describes the Casimir energy between non-parallel cylinders, a geometry not studied until now to our knownledge.