Bloch equations: beyond the raw model
Résumé
The raw Bloch model can be derived rigourously from the Schrödinger or the Heisenberg equation. However to describe complex situations, some terms should be added, or some equations should be coupled, which is performed more or less phenomenologically. The main issues to address then are: which mathematical properties should be asked for extra variables, do the equations still preserve some reasonable physical properties. The same applies for the numerical schemes. In addition to the above mentioned properties, one could ask schemes to behave well in some asymptotic contexts.