Pierfrancesco Di Cintio — Università di Firenze # Transport and diffusion in low dimensional systems with long-range interactions # With the aid of \(N\)-body simulations we study the problems of relaxation and energy transport and diffusion in one dimensional chains of non-linear oscillators with interaction strength decaying with a power \(\alpha\) of their spacing. Moreover, we study the effects of a thermal bath coupled to one or more degrees of freedom of the system for different values of the force exponent \(\alpha\). Results are then compared with those of other long-range models such as for example the \(\alpha\)-HMF model.