Relationships between power-law long-range interactions and fractional mechanics
AbstractWe investigate the relationships between models of power-law long-range interactions and mechanics based on fractional derivatives. We present the fractional Lagrangian density which gives the Euler–Lagrange equation that serves as the equation of motion for fractional-power-law long-range interactions. We derive this equation by the fractional variational method. In addition, we derive a Noether-like current from the fractional Lagrangian density.
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Bibliographic InfoArticle provided by Elsevier in its journal Physica A: Statistical Mechanics and its Applications.
Volume (Year): 391 (2012)
Issue (Month): 23 ()
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Web page: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/
Lattice dynamics; Long-range interaction; Fractional calculus; Fractional variational method;
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- Laskin, N. & Zaslavsky, G., 2006. "Nonlinear fractional dynamics on a lattice with long range interactions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 368(1), pages 38-54.
- Tsallis, Constantino & Mendes, RenioS. & Plastino, A.R., 1998. "The role of constraints within generalized nonextensive statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 261(3), pages 534-554.
- E. K. Lenzi & B. F. de Oliveira & N. G.C. Astrath & L. C. Malacarne & R. S. Mendes & M. L. Baesso & L. R. Evangelista, 2008. "Fractional approach, quantum statistics, and non-crystalline solids at very low temperatures," The European Physical Journal B - Condensed Matter and Complex Systems, Springer, Springer, vol. 62(2), pages 155-158, 03.
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