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Fractional Liouville equation on lattice phase-space

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  • Tarasov, Vasily E.

Abstract

In this paper we propose a lattice analog of phase-space fractional Liouville equation. The Liouville equation for phase-space lattice with long-range jumps of power-law types is suggested. We prove that the continuum limit transforms this lattice equation into Liouville equation with conjugate Riesz fractional derivatives of non-integer orders with respect to coordinates of continuum phase-space. An application of the fractional Liouville equation with these Riesz fractional derivatives to describe properties of plasma-like nonlocal media is considered.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:421:y:2015:i:c:p:330-342
    DOI: 10.1016/j.physa.2014.11.031
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    References listed on IDEAS

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    1. 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.
    2. S. Ruffo, 2008. "Equilibrium and nonequilibrium properties of systems with long-range interactions," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 64(3), pages 355-363, August.
    3. 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.
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    Cited by:

    1. Tarasov, Vasily E., 2021. "Nonlocal quantum system with fractal distribution of states," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 574(C).
    2. 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).
    3. Vasily E. Tarasov, 2024. "Exact Finite-Difference Calculus: Beyond Set of Entire Functions," Mathematics, MDPI, vol. 12(7), pages 1-37, March.

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