Relaxation Dynamics in a Long-Range System with Mixed Hamiltonian and Non-Hamiltonian Interactions

Sometimes the dynamics of a physical system is described by non-Hamiltonian equations motion, and additionally, characterized long-range interactions. A concrete example that particles interacting with light as encountered in free-electron laser cold-atom experiments. In this work, we study relaxation to systems, more precisely, systems interactions both Hamiltonian origin. Our model consists $N$ globally-coupled moving on circle unit radius; one-dimensional. We show infinite-size limit, dynamics, similarly case, Vlasov equation. eventually reaches an equilibrium state, even though one has wait for long time diverging happen. By contrast, there no state expected reach eventually. characterize its average magnetization. find depends strongly relative weight contributions interaction. When part predominant, magnetization attains vanishing value, suggesting does not sustain states constant magnetization, either stationary or rotating. On other hand, when presents long-lived strong oscillations, which provide heuristic explanation. Furthermore, finite-size corrections are much pronounced than those case; justify showing Lenard-Balescu equation, gives leading-order vanish, contrary what occurs one-dimensional systems.