Generalized Kubo relations and conditions for anomalous diffusion: Physical insights from a mathematical theorem

Abstract : The paper describes an approach to anomalous diffusion within the framework of the generalized Langevin equation. Using a Tauberian theorem for Laplace transforms due to Hardy, Littlewood, and Karamata, generalized Kubo relations for the relevant transport coefficients are derived from the asymptotic form of the mean square displacement. In a second step conditions for anomalous diffusion are derived for the asymptotic forms of the velocity autocorrelation function and the associated memory function. Both spatially unconfined and confined diffusion processes are considered. The results are illustrated with semi-analytical examples.
Document type :
Journal articles
Complete list of metadatas

https://hal.archives-ouvertes.fr/hal-00614940
Contributor : Isabelle Frapart <>
Submitted on : Wednesday, August 17, 2011 - 3:18:39 PM
Last modification on : Friday, June 14, 2019 - 3:12:08 PM

Identifiers

Citation

Gerald R. Kneller. Generalized Kubo relations and conditions for anomalous diffusion: Physical insights from a mathematical theorem. Journal of Chemical Physics, American Institute of Physics, 2011, 134 (22), pp.Article Number: 224106. ⟨10.1063/1.3598483⟩. ⟨hal-00614940⟩

Share

Metrics

Record views

79