Condensed concepts

Working in quantum many-body theory, I slowly learned that many key concepts and techniques have predecessors and analogues in classical systems and one-body quantum systems. Examples include Green's functions, path integrals, cumulants, the linked cluster theorem, Hubbard-Stratonavich transformation (completing the square), mean-field theory, localisation due to disorder, and BBGKY hierarchy . Learning a full-blown quantum many-body version is easier if you first understand simpler analogues. This post is about effective theories in classical systems and one-body quantum systems, following my earlier post about effective theories in quantum field theories of elementary particles . Michèle Levi  has a pedagogical article Effective field theories of post-Newtonian gravity: a comprehensive review This is motivated by the use of EFTs to describe gravitational waves produced by the inspiraling and merging of binary black holes and neutron stars . She discusses the different scales invo

The Netflix series, 3-body Problem , features physics and physicists throughout. I am not a big fan of science fiction, but watched the first episode, to try and get a sense of why the series is attracting so much attention. The opening scene (in the video above) is rooted in history. It depicts a "struggle session" during the Cultural Revolution , featuring the denunciation and killing of a physics professor, who is the father of the main character in the series. For some more on the intellectual and political background see Organized criticism of Einstein and relativity in China, 1949–1989 , by Danian Hu

 Over the last hundred years, there has been a fruitful cross-fertilisation of concepts and techniques between the theory of condensed matter and the quantum theory of elementary particles and fields. Examples include spontaneous symmetry breaking, renormalisation, and BCS theory. Sometimes, these efforts have occurred in parallel and only later did people realise that two different communities were doing essentially the same thing but using different language. Other times, one community adopted ideas or techniques from the other. Central to condensed matter theory are ideas of emergence, a hierarchy of scales, and effective theories that are valid at a particular scale. Elementary particle theorists such as Steven Weinberg often distinguish themselves as reductionists with different goals and approaches. I only recently became aware that effective field theories have become a big thing in the elementary particle community, and Weinberg has been one of the leaders of this! There is a h

Stimulated by discussions about the physics of learning machines with Gerard Milburn, I have been wondering about biomolecular machines such as proteins that do the transcription and translation of DNA in protein synthesis.  These are rather amazing machines. I found an article which considers a problem that is simpler than learning, computation. The thermodynamic efficiency of computations made in cells across the range of life Christopher P. Kempes, David Wolpert, Zachary Cohen and Juan Pérez-Mercader It considers the computation of translating a random set of 20 amino acids into a specific string for a specific protein.  Actual thermodynamic values are compared to a generalised Landauer bound for computation .  Below is the punchline. (page 9) Given that the average protein length is about 325  amino acids for 20 unique amino acids, we have that  p i = p =1/20 325 =1.46×10 −423 , where there are 20 325  states, such that the initial entropy is    , which gives the free energy chang

 Recently my wife and I watched the movie, Joe Versus the Volcano , starring Tom Hanks and Meg Ryan. What I did not expect was that making superconductors commercially viable was central to the (silly but amusing) plot.  The plot summary on Wikipedia says a wealthy industrialist named Samuel Graynamore needs "bubaru", a mineral essential for manufacturing superconductors. There are deposits of it on the tiny Pacific island of Waponi Woo, but the resident Waponis will only let him mine it if he solves a problem for them... Here is the relevant scene... The movie was made in 1990, just after the discovery of cuprate superconductors and at that time there was a lot of hype about commercialisation. I wonder if the scriptwriters drew on that.

Three weeks ago I did a local book launch for  Condensed Matter Physics: A Very Short Introduction . It was at a wonderful independent bookstore,  Avid Reader,  It is a vibrant part of the local community and has several author events every week. I had a conversation about the book with my friend,   Dr Christian Heim , an author, composer, and psychiatrist. My wife and daughter were surprised it was so funny. Most people loved it, but a couple of people thought it should have been more technical. I think that is not the point of such an event or of the Very Short Introduction series. Here is a recording of the conversation, including the Q&A with the audience afterwards. Many thanks to all the friends who came.

The concept of emergence is central to understanding sub-fields of physics and how they are related, and not related, to other sub-fields. The table below shows a stratum of sub-disciplines of physics. For each strata there are a range of length, time, and energy scales that are relevant. There are distinct entities that are composed of the entities from lower strata. These composite entities interact with one another via effective interactions that arise due to the interactions present at lower strata and can be described by an effective theory. Each sub-discipline of physics is semi-autonomous. Collective phenomena associated with a single strata can be studied, described, and understood without reference to lower strata. Table entries are not meant to be exhaustive but to illustrate how emergence is central to understanding sub-fields of physics and how they are related to one another. What do you think of the table? Is it helpful? Have you seen something like this before? I welcome

 A characteristic of emergent phenomena in a system of many interacting parts is that they exhibit collective behaviour where it looks like the many parts are "dancing to the same tune". But who is playing the music, who chose it, and who conducts the orchestra? Consider the following examples. 1. A large group of starlings move together in what appears to be a coherent fashion. Yet, no lead starling is telling all the starlings how and where to move, according to some clever flight plan to avoid a predator. Studies of flocking [murmuration] have shown that each of the starlings just moves according to the motion of a few of their nearest neighbours. Nevertheless, the flock does move in a coherent fashion "as if" there is a lead starling or air traffic controller making sure all the planes stick to their flight plan. 2. You can buy a freshly baked loaf of bread at a local bakery every day. Why? Thousands of economic agents, from farmers to truck drivers

Last year I wrote a post about emergence in AI , specifically on a paper claiming evidence for a "phase transition" in Large Language Models' ability to perform tasks they were not designed for. I found this fascinating. That paper attracted a lot of attention, even winning an award for the best paper at the conference at which it was presented. Well, I did not do my homework. Even before my post, another paper called into question the validity of the original paper. Are Emergent Abilities of Large Language Models a Mirage? Rylan Schaeffer, Brando Miranda, Sanmi Koyejo we present an alternative explanation for [the claimed] emergent abilities: that for a particular task and model family, when analyzing fixed model outputs, emergent abilities appear due to the researcher's choice of metric rather than due to fundamental changes in model behavior with scale . Specifically, nonlinear or discontinuous metrics produce apparent emergent abilities, whereas linear or continu

Physical bookstores selling physical books are in decline, sadly. Furthermore, the stores that are left are mostly big chains. Brisbane does have an independent bookstore, Avid Reader, in the West End. It is a vibrant part of the local community and has several author events every week. My daughter persuaded me to do a book launch, for  Condensed Matter Physics: A Very Short Introduction (Oxford UP, 2023)     It is at Avid Reader on Monday, February 26, beginning at 6 pm. Most readers of this blog are not in Brisbane, but if you are or know people who are please encourage them to consider attending. The event is free but participants need to register , as space is limited.   I will be in conversation about the book with my friend,   Dr Christian Heim , an author, composer, and psychiatrist. Like the book, the event is meant for a general audience.   

Two of the approaches to the theoretical description of systems with emergent properties that have been fruitful are effective theories and toy models. These leverage our limited knowledge of many details about a system with many interacting components. Effective theories An effective theory is valid at a particular range of scales. This exploits the fact that in complex systems there is often a hierarchy of scales (length, energy, time, or number). In physics, examples of effective theories include classical mechanics, general relativity, classical electromagnetism, and thermodynamics. The equations of an effective theory can be written down almost solely from consideration of symmetry and conservation laws. Examples include the Navier-Stokes equations for fluid dynamics and non-linear sigma models in elementary particle physics. Some effective theories can be derived by the “coarse-graining” of theories that are valid at a finer scale. For example, the equations of classical mechanic

The hype about AI continues, whether in business or science. Undoubtedly, there is a lot of potential in machine learning, big data, and large language models. But that does not mean that the hype is justified. It is more likely to limit real scientific progress and waste a lot of resources. My innate scepticism receives concrete support from an article from 2018 that gives four scientific reasons for concern. Big data: the end of the scientific method?  Sauro Succi and Peter V. Coveney The article might be viewed as a response to a bizarre article in 2008 by Chris Anderson, editor-in-chief at Wired, The End of Theory: The Data Deluge Makes the Scientific Method Obsolete ‘With enough data, the numbers speak for themselves, correlation replaces causation, and science can advance even without coherent models or unified theories’. Here are the four scientific reasons for caution about such claims given by Succi and Coveney. (i)   Complex systems are strongly correlated, hence they do not

The Ising model is emblematic of “toy models” that have been proposed and studied to understand and describe emergent phenomena. Although originally proposed to describe ferromagnetic phase transitions, variants of it have found application in other areas of physics, and in biology, economics, sociology, neuroscience, complexity theory, …   Quanta magazine had a nice article marking the model's centenary. In the general model there is a set of lattice points {i} with a “spin” {sigma_i = +/-1} and a Hamiltonian where h is the strength of an external magnetic field and J_ij is the strength of the interaction between the spins on sites i and j. The simplest models are where the lattice is regular, and the interaction is uniform and only non-zero for nearest-neighbour sites. The Ising model illustrates many key features of emergent phenomena. Given the relative simplicity of the model, exhaustive studies since its proposal in 1920, have given definitive answers to questions often debat

  David Mermin has posted a preprint with the modest title, Autobiographical Notes of a Physicist There are many things I enjoyed and found interesting about his memories. A few of the stories I knew, but most I did not. He reminisces about his interactions with Ken Wilson, John Wilkins, Michael Fisher, Walter Kohn, and of course, Neil Ashcroft. Mermin is a gifted writer and can be amusing and mischievous. He is quite modest and self-deprecating about his own achievements. He explains why we should refer to the Hohenberg-Mermin-Wagner theorem, not Mermin-Wagner. One of his Reference Frame columns in Physics Today , stimulated Paul Ginsbarg to start the arXiv. I was struck by how Mermin's career belongs to a different era. The community was smaller and more personal. Doing physics was fun. Time was spent savouring the pleasure of learning new things and explaining them to others. Colleagues were friends rather than competitors. His research was curiosity-driven. This led to Mermin

 Discovering new materials with functional properties is hard, very hard. We need all the tools we can from serendipity to high-performance computing to chemical intuition.  At the end of last year, two back-to-back papers appeared in the luxury journal Nature. Scaling deep learning for materials discovery All the authors are at Google. They claim that they have discovered more than two million new materials with stable crystal structures using DFT-based methods and AI. On Doug Natelson's blog there are several insightful comments on the paper about why to be skeptical about AI/DFT based "discovery". Here are a few of the reasons my immediate response to this paper is one of skepticism. It is published in Nature. Almost every "ground-breaking" paper I force myself to read is disappointing when you read the fine print. It concerns a very "hot" topic that is full of hype in both the science and business communities. It is a long way from discovering a st

Best wishes for the New Year! One thing I hope to achieve this year is an actual understanding of things "Bayesian". I am particularly interested because it gives a way to be more quantitative and precise about some of the intuitions that I use in science. For example, I tend to be skeptical of new experimental results (often hyped) that claim to go against well-established theories, regardless of how good the "statistics" of the touted result. In this vein, Phil Anderson argued that  Bayesian methods  should have been used to rule out the significance of "discoveries" such as the 10 keV neutrino and the fifth force. In 1992 he wrote a  Physics Today column on the subject. An interesting metric for mathematical formula is the ratio of profound and wide implications to the simplicity of the formula and its derivation.  I suspect that Bayes' formula for conditional probabilities would win first place! P(A|B) denotes the probability of A given B.  The pr