Condensed concepts

In my last post, I asked a number of questions about Condensed Matter Physics (CMP) that my son asked me. On reflection, my title ``basic questions" was a misnomer, because these are actually rather profound questions. Also, it should be acknowledged that the answers are quite personal and subjective. Here are my current answers. 1. What do you think is the coolest or most exciting thing that CMP has discovered?  Superconductivity. explained? BCS theory of superconductivity. Renormalisation group (RG) theory of critical exponents. 2. Scientific knowledge changes with time. Sometimes long-accepted ``facts''  and ``theories'' become overturned.   What ideas and results are you presenting that you are almost absolutely certain of?  Phase diagrams of pure substances. Crystallography. Landau theory and symmetry breaking as a means to understand almost all phase transitions. RG theory. Bloch's theorem and band theory as a framework to understand the

I am trying out draft chapters of Condensed matter physics: A very short introduction, on a few people who I see as representative of my target audience. My son is an economist but has not studied science beyond high school. He enjoys reading widely. He kindly agreed to give me feedback on each draft chapter. Last week he read the first two chapters and his feedback was extremely helpful. He asked me several excellent questions that he thought I should answer. 1. What do you think is the coolest or most exciting thing that CMP has discovered? explained? 2. Scientific knowledge changes with time. Sometimes long-accepted ``facts''  and ``theories'' become overturned? What ideas and results are you presenting that you are almost absolutely certain of? What might be overturned? 3. What are the most interesting historical anecdotes? What are the most significant historical events? Who were the major players? 4. What are the sexy questions that CMP might answer in th

A recent issue of The Economist has an interesting article about the massive expansion in higher education, both private and public, in Africa. The thing I found most surprising and interesting is the graphic below. It compares the percentage of the population within 5 years of secondary school graduation are enrolled in higher education, in 2000 and 2017. In almost all parts of the world the percentage enrollment has doubled in just 17 years! I knew there was rapid expansion in China and Africa, but did not realise it is such a global phenomenon. Is this expansion good, bad, or neutral? It is helpful to consider the iron triangle of access, cost, and quality . You cannot change one without changing at least one of the others. I think that this expansion is based on parents, students, governments, and philanthropies holding the following implicit beliefs uncritically. Based on the history of universities until about the 1970s. Prior to that universities were fewer, smaller,

Bob Schrieffer died last month, as reported in a New York Times obituary. Obviously, Schrieffer's biggest scientific contribution was coming up with the variational wave-function for the BCS theory of superconductivity. BCS theory was an incredible intellectual achievement on many levels. Many great theoretical physicists had failed to crack the problem. The elegance of the theory was manifest in the fact that it was analytically tractable, yet could give a quantitative description of diverse physical properties in a wide range of materials. BCS also showed the power of using quantum-field-theory techniques in solid state theory. This was a very new thing in the late 50s. Then there was the following cross-fertilisation with nuclear physics and particle physics (e.g. Nambu ). Another significant contribution was the two-page paper from 1966 that used a unitary transformation to connect the Kondo model Hamiltonian to that of the Anderson single impurity model. In particular, it

This is a basic question that I have been puzzling about. I welcome solutions. Consider a diatomic molecule containing atoms with mass m1 and m2. It has a stretch vibration that can be described by a harmonic oscillator with a reduced mass mu given by . Now consider a polyatomic molecule containing N atoms. It will have 3N-6 normal modes of vibration. [The 6 is due to the fact that there are 6 zero-frequency modes: 3 rigid translations and 3 rotations of the whole molecule]. In the harmonic limit, the normal mode problem is solved below. [I follow the classic text Wilson et al., Molecular Vibrations ]. The problem is also solved in matrix form in Chapter 6 of Goldstein, Classical Mechanics ]. One now has a collection of non-interacting harmonic oscillators. All have mass = 1. This is because the normal mode co-ordinates have units of length * sqrt(mass). The quantum chemistry package Gaussian does more. It calculates a reduced mass mu_i for each normal mode i u