Describing the diffusion of brownian correlated objects is not a trivial issue in statistical physics. Long-ranged correlations indeed induce an "anomalous" diffusion, by definition not described by the usual statistical physics laws, which means that it has to be studied on a per cases base. This PhD is devoted to one particular example named Single-file Diffusion, refering to the diffusion of an ordered chain of particles that cannot cross each other. We report here molecular dynamics simulations and experimental results emphasizing the existence of several diffusive behaviors for the longitudinal or transverse fluctuations of particles in a SFD configuration. All our numerical and experimental results can be explained by an analytical model based on the decomposition of the thermal fluctuations on the vibrational eigenmodes of the system. This model can be used to describe real physical systems as it takes into account long-ranged interactions, the influence of the dissipation, the size of the system and the properties of both confinement forces. This eigenmodes analysis can explain the evolution of the transverse fluctuations during the zigzag transition and the structure of the system after the transition. Moreover, studying the transverse fluctuations also contributes to the understanding of the influence of a thermal noise on a pitchfork bifurcation.
