Posts

Effective theories in classical and quantum mechanics

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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

Physics on Netflix

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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

Effective quantum field theories and hierarchial reality

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 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

Is biology better at computing than supercomputers?

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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

Superconductors in Hollywood

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 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.

A light conversation about condensed matter physics

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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.

Emergence and the stratification of physics into sub-fields

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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