Continuous limit of discrete systems with long-range interaction
نویسنده
چکیده
Discrete systems with long-range interactions are considered. Continuous medium models as continuous limit of discrete chain system are defined. Longrange 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. PACS numbers: 45.05.+x, 45.50.−j, 45.10.Hj
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