Friday, August 23, 2019

Basic questions about condensed matter

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 the foreseeable future?

I have some preliminary answers. But, to avoid prejudicing some brainstorming, I will post later.
What answers would you give?

Tuesday, August 20, 2019

The global massification of universities

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, more selective, had greater autonomy (both in governance, curriculum, and research).

1. Most students who graduated from elite institutions went on to successful/prosperous careers in business, government, education, ...

2. Research universities produced research that formed the foundation for amazing advances in technology and medicine, and gave profound new insights into the cosmos, from DNA to the Big Bang.

Caution: the first point does not imply that a university education was crucial to the graduates' success. Correlation and causality are not the same thing. The success of graduates may be just a matter of signaling.  Elite institutions carefully selected highly gifted and motivated individuals who were destined for success. The university just certified that the graduates were ``hard-working, smart, and conformist.''

But the key point is these two observations (beliefs) concern the past and not the present. Universities are different.  Massification and the stranglehold of neoliberalism (money, marketing, management, and metrics) mean that universities are fundamentally different, from the student experience to the nature of research.

According to Wikipedia,
Massification is a strategy that some luxury companies use in order to attain growth in the sales of product. Some luxury brands have taken and used the concept of massification to allow their brands to grow to accommodate a broader market.
What do you think?
Are these the key assumptions?
Will massification and neoliberalism undermine them?

Tuesday, August 13, 2019

J.R. Schieffer (1931-2019): quantum many-body theorist

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 gave a physical foundation for the Kondo model, which at the time was considered somewhat ad hoc.
John Wilkins wrote a nice commentary on the background history and significance of the Schrieffer-Wolff transformation.
The SW transformation is an example of a general strategy of finding an effective Hamiltonian for a reduced Hilbert space. This can also be done via quasi-degenerate perturbation theory. In different words, when one ``integrates out'' the charge degrees of freedom in the Anderson model one ends up with the Kondo model.

There is also the Su-Schrieffer-Heeger model, that is related to Heeger's Nobel Prize in Chemistry. However, although this spawned a whole industry (that I worked in as a postdoc with Wilkins) its originality and significance is arguably not comparable to BCS and SW.

Because of when he was born, like many of the pioneers of quantum many-body theory, Schrieffer may have been born for success?

I am somewhat (scientifically) descended from Schrieffer because I did a postdoc with John Wilkins, who was one of Schrieffer's first PhD students. My main interaction with Schrieffer was during 1995-2000. Each year I would visit my collaborator, Jim Brooks, at the National High Magnetic Field Laboratory, and would have some helpful discussions with Schrieffer. During one of those visits, I stumbled across a compendium of reprints from a Japanese lab. [This was back in the days when some people snail-mailed out such things to colleagues]. It had been sent to Schrieffer and contained a copy of a paper by Kino and Fukuyama on a Hubbard model for organic charge transfer salts. That was the starting point for my work on that topic.

Tuesday, August 6, 2019

What is the mass of a molecular vibration?

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 using the formula below.
This is discussed in these notes on the Gaussian web site. From mu_i and the normal mode frequency_i it then calculates the spring constant for each normal mode.

I have searched endlessly, and tried myself, but have not been able to answer the following basic questions:

1. How do you derive this expression for the reduced mass?
2. Is this reduced mass physical, i.e. a measurable quantity?

Similar issues must also arise with phonons in crystals.

Any recommendations?