Investigación

 

Fractional drude model of electrons in a metal

 

M. Guía, J.J. Rosales, L. Martínez, and J.A. Álvarez

 

División de Ciencias e Ingenierías Campus Irapuato-Salamanca, Universidad de Guanajuato, Carretera Salamanca-Valle de Santiago, km. 3.5 + 1.8 km. Comunidad de Palo Blanco, Salamanca, Guanajuato.

 

Received 3 August 2015;
accepted 8 December 2015

 

Abstract

In the present work we analyse the behaviour of electrons in a metal placed into uniform electric field, E, from its fractional differential equation. We show that the velocity and the current density of the electrons not only depend on the time t, but also on the order of the fractional differential equation γ, the Drude model is a particular case. This fact could have interesting consequences in the study of electrical properties of metals.

Keywords: Fractional derivative; drude model; Mittag-Leffler function.

PACS: 45.10.Hj; 45.20.D; 66.70.Df

 

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Acknowledgments

This research was partially supported by DAIP-UGTO under the Grant: 629/2015.

 

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