Sub-diffusive behavior in the Standard Map

Autor(es)

Palmero, Matheus S. ^[1] ; Diaz, I, Gabriel ; Caldas, Ibere L. ^[2] ; Sokolov, Igor M. ^[3]

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo, Inst Fis, Sao Paulo, SP - Brazil

^[2] Diaz, Gabriel, I, Univ Sao Paulo, Inst Fis, Sao Paulo, SP - Brazil

^[3] Humboldt Univ, Inst Phys, Berlin - Germany

• Tipo de documento: Artigo Científico
• Fonte: European Physical Journal-Special Topics; v. 230, n. 14-15, p. 2765-2773, OCT 2021.
• Citações Web of Science: 1

Resumo

In this work, we investigate the presence of sub-diffusive behavior in the Chirikov-Taylor Standard Map. We show that trajectories started from special initial conditions, close to unstable periodic orbits, exhibit sub-diffusion due to stickiness, and can be modeled as a continuous-time random walk. Additionally, we choose a variant of the Ulam method to numerically approximate the Perron-Frobenius operator for the map, allowing us to calculate the exponent of anomalous diffusion by solving an eigenvalue problem and comparing its time dependence to the solution of the fractional diffusion equation. The results here corroborate other findings in the literature of anomalous transport in Hamiltonian maps and can be suitable to describe transport properties of other dynamical systems. (AU)

• Processo FAPESP: 18/03000-5 - Transporte caótico em mapas simpléticos: Aplicações em plasmas
• Beneficiário: Matheus Palmero Silva
• Modalidade de apoio: Bolsas no Brasil - Doutorado
• Processo FAPESP: 18/03211-6 - Dinâmica não linear
• Beneficiário: Iberê Luiz Caldas
• Modalidade de apoio: Auxílio à Pesquisa - Temático