Volume 117, Number 5, March 2017
|Number of page(s)||5|
|Published online||08 May 2017|
Structural scale q-derivative and the LLG equation in a scenario with fractionality
1 Universidade Federal Rural do Rio de Janeiro, UFRRJ-IM/DTL - Av. Governador Roberto Silveira s/n Nova Iguaçú, 695014, Rio de Janeiro, Brasil
2 Centro Brasileiro de Pesquisas Físicas-CBPF - Rua Dr Xavier Sigaud 150, 22290-180, Rio de Janeiro, RJ, Brasil
Received: 2 March 2017
Accepted: 11 April 2017
In the present contribution, we study the Landau-Lifshitz-Gilbert equation with two versions of structural derivatives which were recently proposed: the scale q-derivative in the non-extensive statistical mechanics and the axiomatic metric derivative. The latter presents the Mittag-Leffler functions as eigenfunctions. The use of structural derivatives aims to take into account long-range forces, possible non-manifest or hidden interactions and the dimensionality of space. Having this purpose in mind, we build up an evolution operator and a deformed version of the LLG equation. Damping in the oscillations naturally shows up without an explicit Gilbert damping term.
PACS: 02.90.+p – Other topics in mathematical methods in physics (restricted to new topics in section 02) / 05.90.+m – Other topics in statistical physics, thermodynamics, and nonlinear dynamical systems (restricted to new topics in section 05) / 11.10.Lm – Nonlinear or nonlocal theories and models
© EPLA, 2017
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