Continuous Limit of Discrete Systems with Long-Range Interaction
Classical Physics
2018-04-02 v1
Abstract
Discrete systems with long-range interactions are considered. Continuous medium models as continuous limit of discrete chain system are defined. Long-range interactions of chain elements that give the fractional equations for the medium model are discussed. The chain equations of motion with long-range interaction are mapped into the continuum equation with the Riesz fractional derivative. We formulate the consistent definition of continuous limit for the systems with long-range interactions. In this paper, we consider a wide class of long-range interactions that give fractional medium equations in the continuous limit. The power-law interaction is a special case of this class.
Cite
@article{arxiv.0711.0826,
title = {Continuous Limit of Discrete Systems with Long-Range Interaction},
author = {Vasily E. Tarasov},
journal= {arXiv preprint arXiv:0711.0826},
year = {2018}
}
Comments
23 pages, LaTeX