Condensed concepts

In 1935 Schrodinger wrote his famous paper (with the cat ) introducing the term entanglement, in response to the Einstein-Podolsky-Rosen paper published earlier that year. When Schrodinger wrote the paper he was living in a house on Northmoor Road , Oxford. This was the same house where Schrodinger learned he had been awarded the Nobel Prize. I recently learned some fascinating historical trivia. Schrodinger was a neighbour of J.R.R. Tolkien , who during that time was finishing up work on The Hobbit. It would be nice to see this landmark honoured, such as the one on Tolkien's house. However, it seems Schrodinger's house does not meet the criteria of  Oxfordshire Blue Plaques Board , because he lived there for three years, less than the required minimum of five years. Another option would be a plaque of the Institute of Physics, such as this one.

This is not based on the hubris of a condensed matter physicist, but rather the claim of three economists in an Econtalk  podcast ,  where  Don Boudreaux , Michael Munger , and Russ Roberts  discuss Emergent Order. For example, Boudreaux states the notion of spontaneous order is indeed the most profound, single most profound insight of good economics . It remains the insight that is most elusive to the general public. Sadly, it remains an insight that is elusive to a lot of professional economists these days. The discussion centres around Robert's poem, "Its a wonderful loaf" , the website for which has an animation of the poem and  a nice list of related resources . The key idea is that free markets lead to an emergent order of prices, division of labour, and matching of supply and demand. This order is Adam Smith's "invisible hand" that guides the economy. It is actually "bottom up", not top down. Many of the ideas discussed are those originat

I have received positive feedback about previous posts about mental health and so I share some recent experiences in the hope it may be helpful to some. I have had three significant times where my mental health deteriorated to the point I could not function “normally”. The first was during my Ph.D and the second about 15 years ago. The most recent experience was roughly six months ago. Here are a few things I learnt [or re-learnt] from this last experience. The decline is often gradual and not perceived or denied. It is like the proverbial frog in boiling water. It does not notice how the temperature is increasing and never jumps out. The longer you wait to address the issue the slower the recovery. Don't think things will get better on their own. Mental illness is irrational. That's the point. When I now think about some of the thoughts and perceptions that seemed “real” and “true” to me 6-12 months ago it is sad and bizarre. Relapse is not uncommon. If you have

I learned a lot from reading In the Eye of the Storm : The Autobiography of Sir John Houghton (with Gill Tavner). He is arguably best known for being the lead editor of the first three reports of the IPCC ( Intergovernmental Panel on Climate Change ). He started his scientific life as an atmospheric physicist at Oxford. Here are a few things that struck me. The value of development of new instruments. At Oxford Houghton was largely involved in finding new ways to use rocket based instruments measure the temperature and composition of the atmosphere at different heights. These were crucial for getting accurate data that revealed the extent of climate change and understanding climate dynamics. It was good for me to read this. As a theorist, I am often skeptical or at least unappreciative of the value of developing new instruments. I think it is partly because I have heard too many talks about instrument design where it really wasn't clear they were going to generate useful and re

Many of the most interesting materials involve significant chemical and structural complexity. Indeed, it is not unusual for a unit cell for a crystal to contain the order of one hundred atoms. Yet, for a given class of materials, one would like to find an effective Hamiltonian involving as few degrees of freedom and parameters as possible. Following Kino and Fukuyama, twenty years ago I argued that the simplest possible effective Hamiltonian for a large class of superconducting organic charge transfer salts was a one-band Hubbard model on an anisotropic triangular lattice at half filling. It seemed natural to then argue that the relevant model for the spin degrees of freedom in the Mott insulating phase is the corresponding frustrated Heisenberg model with spatial anisotropy determined by the anisotropy in the tight-binding model. However, it turns out this is not the case. There are some subtle quantum interference effects that I overlooked in the "derivation"  of t

Dimitri Mendeleev , who proposed the periodic table of the elements, purely from phenomenology and without quantum mechanics! He even successfully predicted the existence of new elements and their properties. A friend who is a high school teacher [but not a scientist] asked me about how he should teach the periodic table to chemistry students. It is something that students often memorise, especially in rote-learning cultures, but have little idea about what it means and represents. It makes logical sense, even without quantum mechanics. This video nicely captures both how brilliant Mendeleev was and the logic behind the table. A key idea is how each column contains elements with similar chemical and physical properties and that as one goes down the column there are systematic trends. It is good for students to see this with their own eyes. This video from the Royal Society of Chemistry shows in spectacular fashion how the alkali metals are all highly reactive and that as one g

In the book Who Got Einstein's Office? , about the Institute for Advanced Study at Princeton, the author Ed Regis, mocks it as the "One True Platonic Heaven" because he claims its members are Platonic idealists, who are interested in pure theory, and disdain such "impurities" as computers and applied mathematics. Platonic solids This stimulated me to think about the limited but useful role of pure mathematics, Platonic idealism, and aesthetics in solid state theory. People seem particularly excited when topology and/or geometry plays a role. The first example I could think of is the notion of a perfect crystal. Then comes Bloch's theorem, which surely is the central idea of introductory solid state physics. The icosahedron is central to quasi-crystals. Beautiful examples where advanced pure maths plays are role are Chern-Simons theory of edge states in the Quantum Hall Effect and topological terms in the action for quantum spin chains,