I thought the classroom discussions yesterday on "parallel" and "non-parallel" (serial) mechanisms for conduction were interesting. A student (R, I think) thought that a certain way of thinking about it was more natural for a situation and a certain other way of thinking about it was more natural for another situation. My take is that, deep down, he was grasping what was going on, but he could not articulate about it in a short time. However, articulating is a crucial thing to do. So, let us have some more discussions here, shall we?

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Q: Why is it that resistivities, not conductivities, due to different channels of scattering add up for a charge carrier? Here, different channels of scattering include, e.g., scattering with impurities, scattering with lattice vibrations (so-called phonons), and scattering with other charge carriers.

-- Sam, 4-29, 9:33

A: To me, it makes sense that an electron in an idealized, perfect lattice would have nothing to hinder it. The lattice would be superconducting. Then, if you introduce some hindrance to the electron, crystal impurities, for example, the electron would have a certain probability $P_{1}$ of being scattered by those impurities. If you add another entity to impede the electron, such as vibrations due to heat, the electron may have a probability $P_{2}$ of being scattered by that. The electron may have some further probability $P_{3}$ of being scattered by other electrons in its path and so forth. All of these scattering probabilities can be looked at as individual resistances, and the total resistance a charge carrier experiences is the total probability of it being scattered, $P_{1}+P_{2}+P_{3}$. This is how I think of it.

--Chris, 5-2, 7:00

Yes, that is excellent – any other thoughts by any other people? Nobody's idea is perfectly inclusive, and there may be other ways to think. Side remark: By the way, this way of thinking does entail the notation that each scattering event is Marcovian (no correlation between successive scattering events). This sounds like a reasonable approximation at first (and it is for many cases), but you may also be saying "how can that always be?". Indeed, there are non-Marcovian processes, some mildly so and some completely dramatically so.

-- Sam, 5-8, 2:11PM