Résumé
In the first part we will show a study of the Casimir torque between two metallic one-dimensional gratings rotated by an angle θ with respect to each other. We find that, for infinitely extended gratings, the Casimir energy is anomalouslydiscontinuous at θ = 0, due to a critical zero-order geometric transition between a 2D- and a 1D-periodicsystem. We will comment on the relevant implication of this finding.In the second part I will discuss the Radiative heat transfer (RHT) and radiative thermal energy (RTE) for two-dimensional (2D) nanoparticle ensembles in the framework of many-body radiative heat transfer theory. We consider nanoparticles made of different materials: metals (Ag), polar dielectrics (SiC), or insulator-metallic phase-change materials(VO2). We start by investigating the RHT between two parallel 2D finite-size square-lattice nanoparticleensembles, with particular attention to many-body interactions (MBI) effects. We fix the particle radius (a)as the smallest length scale, and we describe the electromagnetic scattering from particles within the dipoleapproximation. Depending on the minimal distance between the in-plane particles (the lattice spacing p forperiodic systems), on the separation d between the two lattice and on the thermal wavelength,we systematically analyze the different physical regimes characterizing the RHT. Four regimes are identified,rarefied regime, dense regime, non-MBI regime, and MBI regime, respectively.