Introducing physical relaxation terms in Bloch equations

Brigitte Bidégaray-Fesquet (1) , Antoine Bourgeade (2) , Didier Reignier (1)

1 MIP - Mathématiques pour l'Industrie et la Physique
2 CESTA - Centre d'études scientifiques et techniques d'Aquitaine

The Bloch equation models the evolution of the state of electrons in matter described by a Hamiltonian. To model more physical phenomena we have to introduce phenomenological relaxation terms. The introduction of these terms has to conserve some positiveness properties. The aim of this paper is to review possible relaxation models and to provide insight into how to discretize them properly in view of numerical computations.

Keywords: Bloch equations; Relaxation terms; Quantum optics

Domains: Numerical Analysis [math.NA]; Mathematical Physics [math-ph]

Brigitte Bidégaray-Fesquet, Antoine Bourgeade, Didier Reignier. Introducing physical relaxation terms in Bloch equations. Journal of Computational Physics, 2001, 170 (2), pp.603-613. ⟨10.1006/jcph.2001.6752⟩. ⟨hal-00453872⟩