The subject of this thesis is about the numerical computations of two influent quantum observables at the nanoscale : the Casimir force and the radiative heat transfer. In near field, these two physical quantities are at the origin of numerous potential applications in the field of nano-engineering. They are theoretically and experimentally well evaluated in the case of simple geometries such as Fabry-Pérot cavities, which consist in two parallel plane mirrors separated by vacuum. But in the case of the more complex geometries which are unavoidably encountered in practical nanotechnological applications, the electromagnetic modes from which they are derived are subject to scattering processes which make their evaluation considerably more complex. This is for instance the case of NEMS and MEMS, whose general architecture is often non-trivial and highly dependent on the Casimir force and radiative heat flux, with for example the often encountered problem of stiction in these nano-devices. In this thesis I mainly focus on corrugated periodic profiles, which bring important constraints on the simplicity of the computations associated with these observables. After a fundamental review of the mathematical foundations of an exact method of computation of the Casimir force and of the heat flux based on scattering theory, I present in the second part of this thesis the results of the numerical calculations of these quantities for corrugated profiles of various geometrical parameters and for different materials. In particular, I obtain the very first exact results of the out-of-thermal equilibrium Casimir force and of the radiative heat flux between corrugated surfaces. I conclude with a proposal for the design of a thermal modulator device for nanosystems based on my results.
