Classical Goldstone modes in Long-Range Interacting Systems
Abstract
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 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.
Cite
@article{arxiv.2005.03202,
title = {Classical Goldstone modes in Long-Range Interacting Systems},
author = {Tarcisio M Rocha Filho and Bruno Marcos},
journal= {arXiv preprint arXiv:2005.03202},
year = {2020}
}