Nonlinear fractional dynamics on a lattice with long range interactions
By Nick Laskin, George Zaslavsky. 2005
133 citations recorded by the source corpus.
A unified approach has been developed to study nonlinear dynamics of a 1D lattice of particles with long-range power-law interaction. A classical case is treated in the framework of the generalization of the well-known Frenkel–Kontorova chain model for the non-nearest interactions. Quantum dynamics is considered following Davydov's approach for molecular excitons.
Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/982fdfdb643e8a3a95ebafc27e802653a2f237a4
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In Atomic and Molecular Physics, and Optics
In Statistical and Nonlinear Physics
Citations in the corpus
- Fractional Vector Calculus and Fractional Maxwell's Equations (2008, background): “operties (with a nonlocal interaction of medium particles) can be described by the FVC. The fractional derivatives in equations can be connected with a long-range power-law interaction of the systems [37, 38, 40]. The nonlocal properties of electrodynamics can be considered [39] as a result of dipol”
- Review of Some Promising Fractional Physical Models (2013, background): “As it was shown [50, 51, 52, 53, 54, 55, 56, 57, 58], the equations with fractional derivatives can be directly connected to chain and lattice models with long-range interactions.”