Electron Charge and Current Densities, the Geometrie Phase and Cellular Automata*

Some consequences of the quan tum fluid dynamics formulation are discussed for excited states of a toms and molecules and for time-dependent processes. It is shown that the conservation of electronic current density j(r) allows us to manufacture a gauge potential for each excited state of an atom, molecule or a tom in a molecule. This potential gives rise to a tube of magnetic flux carried around by the many-electron system. In time-dependent situations, the evolution of the electronic density distribution can be followed with simple, site-dependent cellular automaton (CA) rules. The CA consists of a lattice of sites, each with a finite set of possible values, here representing finite localized elements of electronic charge and current density (since the charge density Q no longer suffices to fully characterize a time-dependent system, it needs to be supplemented with information about the current density j). Our numerical results are presented elsewhere and further development is in progress.