I noticed before yesterday’s lecture on Boltzmann theory, that I need to at least remind what the Fermi Golden Rule is (I made a video of the derivation), and to explain again the relation between the chemical potential, Fermi energy and the electrostatic potential. This took so much time that I barely reached the diffusive limit of the Boltzmann equation. It is a pity: it would have been better to show how one can, with consequent simplifications, always assuming that scattering breaks a certain symmetry (or conservation law), reach an increasingly simplified equation describing the state of the particles. This seems to be a “general know-how” of researchers in the field, but I had not seen it explained before, so I wanted to include it in my book. Eventually one gets only the diffusion equation for the (electro)chemical potential, which is what you would get from Ohm’s law.
Even that simplest limit, however, can be interesting if we allow for a spin-dependent potential, and in some portions of the structure spin-dependent conductivities arising from spin-dependent densities of states (in ferromagnets). The behavior of the charge current/resistance in this system is at the heart of spintronics. In my book I only discuss collinear magnetizations and fields. The non-collinear case would also be interesting, because it would allow discussing the spin Hanle effect, and possibly the spin transfer torque that will be used in future devices of spintronics. Perhaps in the next edition of the book I will devote an entire chapter for spintronics… If there will ever be the next edition, though.
So now I have the dilemma whether to try to use part of the project lecture tomorrow for finishing the Boltzmann lecture, or whether to delay my schedule and give the rest of the lecture on Tuesday. Probably I will do the latter, and then later catch up, so that the projects get going better.