Attraction and friction forces between identical revolving atoms mediated by the electromagnetic vacuum

The understanding of dissipation is a crucial point for the description of physical phenomena, at any scale. However, as pointed out by Loschmidt, if we describe the microscopic world through time-reversible laws, how is it possible to observe irreversibilities at our macroscopic scale, in particular the second law of thermodynamics? A first element of the answer, derived from the static effect highlighted by Casimir, is to consider the dynamical interaction of matter with its environment, in particular with the electromagnetic vacuum, inescapable quantum background. The motion of objects interacting with such fluctuating medium undergoes perturbations and a friction may arise, which is the starting point of the study of quantum friction effects. Here, I focused on a special case: two identical atoms, attracted to each other by a dispersion force mediated by the vacuum fluctuations, revolving around each other on a circular trajectory. This configuration, which can occur in soft collisions with large impact parameters, typically inside fluids, is of great theoretical interest since it physically justifies the calculation of attractive forces without modifying the interatomic distance. The aim of this study was to build a semi-classical analysis of the problem, allowing to compute exactly the force exerted on each of the atoms. To begin with, I established the classical model for the atom, involving the notion of radiation reaction, of high importance for the self-consistency as well as the stability of matter when plunged inside the fluctuations of the vacuum field possessing (infinite) zero point energy. Then, I described the thermal vacuum electromagnetic field throughout its correlations, including the dynamical effects, allowing me to remain within a classical formalism. The dynamics of the two atoms on their circular trajectory is thereafter described with a quasi-steady state picture, making possible the use of Fourier transforms on the atomic dipole moments. This description allows then the calculation of effective polarizabilities, due to interatomic coupling, which model the induction by the vacuum field. The forces exerted on the atomic centers of mass are therefore written as integrals of quadratic forms of the thermal vacuum electromagnetic field in frequency domain, which allows for the use of the previously derived correlations. Hence, I managed to compute explicitly the interatomic attraction force, which I was able to recover the literature results, especially the ones of London and Casimir-Polder, henceforth validating the consistency of the model. Finally, I considered the dissipation through the calculation of a friction force exerted on the atoms, depending on both the temperature of the thermal vacuum blackbody radiation and the interatomic distance. The single atom friction result, when moving relatively to the reference frame of the blackbody, as studied by Einstein and Hopf, is also recovered. A key point of the work was to calculate the quantum friction, i.e. the braking force exerted on the rotating pair of atoms by the electromagnetic vacuum at zero temperature. The complete resolution of the system within the framework of the model results in zero friction, contrary to the partial and preliminary result of 2015. However, in the context of an improved quantum electrodynamics resolution, the introduction of a cut-off in the integral over the frequencies would reveal non-zero friction.