Dynamics of two harmonically coupled Brownian particles with memory

Abstract

We consider two coupled Brownian oscillators with memory. Exact expressions for the position x_i(t), velocity v_i(t), their variances 〈Δx_i²(t)〉  and 〈Δv_i²(t)〉, and the diffusion coefficient D_i(t) are calculated. Our results show that there is a superdiffusive behavior observed in the system due to the coupling of the Brownian oscillators. Beyond this superdiffusive regime, the particles behave subdiffusively.