The idea of this blog, if that’s what it is, came to me in this way. Over the last decade or so, I’d been thinking about a number of condensed matter physics problems, some to do with electron spectroscopy of various kinds but many relating to electron dynamics. The traditional approach of band theory (Kohn-Sham density functional theory etc) deals mainly with static electronic structure properties such as total energies, phase stability, structure and bonding – the properties whose study has now evolved into the field of “computational materials science”. The thought I had was that, given (pulsed) photon sources such as (free electron) lasers, you could see the electrons in motion, as it were. Perhaps you could watch the electrons directly in time, as they took part in interesting processes, rather than inferring dynamics indirectly from observations in the energy domain, as spectroscopic methods usually force you to do. The new sources promised time-resolution down to the attosecond scale; the atomic unit of time, the typical time scale of electronic motions in atomic systems, is about 24 As.

This led me to try to learn about quantum dynamics – essentially solving the time-dependent Schrödinger equation, in different physical contexts and with different techniques. In doing this, I found that I needed to re-learn quite a lot of standard quantum mechanics, trying to achieve a deeper understanding of things I thought I knew. I also hoped to appreciate (finally) aspects which have come to assume greater prominence in modern quantum mechanics than when I first learned the subject – symmetry breaking, entanglement, Berry’s phase and so on – not just because of their intellectual interest but also because they play a central role in modern solid state physics. I wrote extensive notes for myself, and it occurred to me that some of this material might serve as an informal introduction to others following the same path as me.

I also found myself working out some toy models, which I thought quite interesting in their own right, but which also possessed a pedagogical value as a source of insight into more serious problems. It occurred to me that a blog like this might be a good vehicle to make such material available to others. I wanted to do this a more relaxed and informal way than proper publication requires. In any case, what I had in mind was not suitable for publication in research journals – it’s not novel research at all, really, but rather a kind of personal diary of things you learn in the course of trying to do research, things that are perhaps not too widely known.

So that’s what I had in mind. This form of communication is new to me and I’ll be feeling my way into it. Some of the stuff I’ll post will be talks – lots of pictures and results, but the real theory behind it is a bit cryptic. Other stuff will be more theory-based – the details worked out properly, but fewer pictures. I might even include some historical stuff, just for fun. I will give a very brief outline of each topic, by way of an introduction. Here goes.

A note note on references
Occasionally I refer to other sets of notes I’ve compiled or to other posts in this series. This leads to entries such as the following in my References list:
[1] Maths Notes.doc, PJD (DL 2020)
[2] “On wave-packet dynamics”, post 3 in this series, PJD (DL 2020)

Here [2] is self-explanatory. [1] refers to my private general maths notes – these kinds of private notes are almost all standard book work, collected according to my own needs, but if anyone would like access to them, please ask me.

Paul Durham