Sunday, December 08, 2019

Brief items

Here are some tidbits that came across my eyeballs this past week:

  • I just ran into this article from early in 2019.  It touches on my discussion about liquids, and is a great example of a recurring theme in condensed matter physics.  The authors look at the vibrational excitations of liquid droplets on surfaces.  As happens over and over in physics, the imposition of boundary conditions on the liquid motion (e.g., wetting conditions on the surface and approximately incompressible liquid with a certain surface tension) leads to quantization of the allowed vibrations.  Discrete frequencies/mode shapes/energies are picked out due to those constraints, leading to a "periodic table" of droplet vibrations.  (This one looks moderately like atomic states, because spherical harmonics show up in the mode description, as they do when looking at atomic orbitals.)
  • Another article from the past, this one from 2014 in the IEEE Spectrum.  It talks about how we arrived at the modern form for Maxwell's equations.  Definitely a good read for those interested in the history of physics.  Maxwell's theory was developing in parallel with what became vector calculus, and Maxwell's original description (like Faraday's intuition) was very mechanistic rather than abstract.
  • Along those lines, this preprint came out recently promoting a graphical pedagogical approach to vector calculus.  The spirit at work here is that Feynman's graphical diagrammatic methods were a great way to teach people perturbative quantum field theory, and do perhaps a diagrammatic scheme for vector calc could be good.  I'm a bit of a skeptic - I found the approach by Purcell to be very physical and intuitive, and this doesn't look simpler to me.
  • This preprint about twisted bilayer graphene and the relationship between superconductivity and strongly insulating states caught my eye, and I need to read it carefully.  The short version:  While phase diagrams showing superconductivity and insulating states as a function of carrier density make it tempting to think that SC evolves out of the insulating states via doping (as likely in the cuprates), the situation may be more complicated.


Don Monroe said...

As an MIT physics undergraduate in the late 70s, I learned vector calcululus from Div, Grad, Curl, and All That,", which I found both enjoyable and useful.

Douglas Natelson said...

I thought about putting that one down, but I’ve never used it myself.

Anonymous said...

Since you mention pedagogy and liquids, what about good texts to get physicists comfortable with fluid/continuum dynamics?

This topic has long been dropped from the standard curriculum, and I don't know of a good standalone pedagogical text on the topic for physics use. Landau+Lifshitz doesn't count!

Douglas Natelson said...

Anon, I’ve been wracking my brain trying to remember what we used in grad school - I think it might’ve been the second half of Fetter and Walecka and the LL book on elasticity. I actually rather like the approach in Kip Thorne’s new mega-tome, but the book is cumbersome to say the least. For basic fluid mechanics, I used Fox and McDonald as a sophomore engineer, but it’s not what I would call physicsy. Perhaps there is an opportunity for a pedagogical book on this aimed at, say, senior undergraduates. I agree that it’s very weird how little of this is in the standard curriculum. This is an observation made by others, too:
Anyone out there got any good suggestions?

Douglas Natelson said...

I will say that this is quite pedagogical, though perhaps not what everyone might have in mind: