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arXiv · 0711.0826

Continuous Limit of Discrete Systems with Long-Range Interaction

Vasily E. Tarasov
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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.

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Vasily E. Tarasov. 2007-11-06. Continuous Limit of Discrete Systems with Long-Range Interaction. https://doi.org/10.1088/0305-4470/39/48/005

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