Eur. Phys. J. D (2015) 69: 25
https://doi.org/10.1140/epjd/e2014-50158-7

Regular Article

On the contribution of exchange interactions to the Vlasov equation^*

¹ Department of Physics, Umeå University, 90187 Umeå, Sweden
² Department of Applied Physics, Division for Condensed Matter Theory, Chalmers University of Technology, 41296 Göteborg, Sweden

^a e-mail: mattias.marklund@physics.umu.se

Received: 28 February 2014
Received in final form: 10 June 2014
Published online: 21 January 2015

Abstract

Exchange effects play an important role in determining the equilibrium properties of dense matter systems, as well as for magnetic phenomena. There exists an extensive literature concerning, e.g., the effects of exchange interactions on the equation of state of dense matter. Here, a generalization of the Vlasov equation to include exchange effects is presented allowing for electromagnetic mean fields, thus incorporating some of the dynamic effects due to the exchange interactions. Treating the exchange term perturbatively, the correction to classical Langmuir waves in plasmas is found, and the results are compared with previous work. It is noted that the relative importance of exchange effects scales similarly with density and temperature as particle dispersive effects, but that the overall magnitude is sensitive to the details of the specific problem. The implications of our results are discussed.