2020/05/31 by Tarcisio M Rocha Filho, Bruno Marcos
Physics and Astronomy · #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.102.032122
published as Phys. Rev. E 102, 032122 (2020)
arxiv created 2020/07/22 · arxiv updated 2020/09/23
For a classical system with long-range interactions, a soft mode exists whenever a stationary state spontaneously breaks a continuous symmetry of the Hamiltonian. Besides that, if the corresponding coordinate associated to the symmetry breaking is periodic, the same energy of the different stationary states and finite N thermal fluctuations result in a superdiffusive motion of the center of mass for total zero momentum, that tends to a normal diffusion for very long-times. As examples of this, we provide a two-dimensional self-gravitating system, a free electron laser and the Hamiltonian Mean-Field (HMF) model. For the latter, a detailed theory for the motion of the center of mass is given. We also discuss how the coupling of the soft mode to the mean-field motion of individual particles may lead to strong chaotic behavior for a finite particle number, as illustrated by the HMF model.