Consider two atoms of platinum, A and B, in a sample of platinum. Atom A lives deep within the sample, and atom B lives at the tip of a sharp protuberance at the surface. My understanding is that electrons in the sample will accumulate within a surface defect such as the tip of a sharp needle. The following questions come up for me (not necessary to address here, but you can if you like): In the equilibrium case, what is the range of variation in electron density in the volumes on the atomic scale immediately surrounding A and B? In the non-equilibrium case, where there is a dynamic perturbation such as the application of a strong time varying electric potential or magnetic field, what is the range in variation in electron density? What are the average differences and what are the minima and maxima over time? Are these questions that have been explored experimentally, or are they ones that are accessible only through modeling? In this context my question for this forum is: is there a textbook or a set of papers that can help me to become acquainted with what is known about the dynamic, non-equilibrium case, where there is a perturbation of some kind?