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Energy levels of complex systems: background


The ground state energy of a hard-sphere Bose gas - Elliot Lieb
Freeman Dyson Scientist
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This is another of these beautiful problems which is mathematically well-defined. If you have a... a gas of hard spheres with no other interactions except just excluded volume, each sphere excludes its neighbours by a certain distance; the question is: what's the ground state energy? That's the simplest problem you can ask, at zero temperature, when everything is as close to zero motion as it can possibly be: what's the energy? And there is a famous conjecture, which I think it was due to Yang, or maybe Yang and Lee together, that says the ground state energy per particle is 4pi rho a where 4p times the density(p) times the radius(a), in suitable units, and everybody believes that that's true. It was actually proved only this last year by Elliot Lieb and one of his students. So it's taken fifty years or so actually to prove it. It's a beautiful piece of work. Finally, Lieb... I mean Lieb is, of course, the master craftsman in this particular field, and finally he was able to do it, but again by a very elegant and difficult piece of mathematics. I was not able to do that. I managed to get a lower bound on the energy which at least was of the right order of magnitude. It was too small by a factor of about twelve, so I came within a factor of twelve of the right answer. So I didn't solve the problem, but at least I made some substantial progress. And I'm happy that Lieb finally has smashed it.

Freeman Dyson (1923-2020), who was born in England, moved to Cornell University after graduating from Cambridge University with a BA in Mathematics. He subsequently became a professor and worked on nuclear reactors, solid state physics, ferromagnetism, astrophysics and biology. He published several books and, among other honours, was awarded the Heineman Prize and the Royal Society's Hughes Medal.

Listeners: Sam Schweber

Silvan Sam Schweber is the Koret Professor of the History of Ideas and Professor of Physics at Brandeis University, and a Faculty Associate in the Department of the History of Science at Harvard University. He is the author of a history of the development of quantum electro mechanics, "QED and the men who made it", and has recently completed a biography of Hans Bethe and the history of nuclear weapons development, "In the Shadow of the Bomb: Oppenheimer, Bethe, and the Moral Responsibility of the Scientist" (Princeton University Press, 2000).

Tags: Elliot Lieb, TD Lee, CN Yang

Duration: 2 minutes, 6 seconds

Date story recorded: June 1998

Date story went live: 24 January 2008