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Relationships between power-law long-range interactions and fractional mechanics

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  • Ishiwata, Ryosuke
  • Sugiyama, Yūki

Abstract

We 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.

Suggested Citation

  • Ishiwata, Ryosuke & Sugiyama, Yūki, 2012. "Relationships between power-law long-range interactions and fractional mechanics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(23), pages 5827-5838.
    • Handle: RePEc:eee:phsmap:v:391:y:2012:i:23:p:5827-5838
    DOI: 10.1016/j.physa.2012.06.055
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    References listed on IDEAS

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    1. 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;EDP Sciences, vol. 62(2), pages 155-158, March.
    2. 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.
    3. 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.
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    Cited by:

    1. Tarasov, Vasily E., 2015. "Fractional Liouville equation on lattice phase-space," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 421(C), pages 330-342.
    2. Tarasov, Vasily E., 2015. "Lattice fractional calculus," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 12-33.
    3. Tarasov, Vasily E., 2021. "Nonlocal quantum system with fractal distribution of states," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 574(C).
    4. Tarasov, Vasily E., 2023. "Nonlocal statistical mechanics: General fractional Liouville equations and their solutions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 609(C).

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