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My work with Mehta is now more relevant


Inviting Mehta to work on circular ensembles
Freeman Dyson Scientist
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And so I got interested in that and invited Mehta to come here to Princeton and work with me, and so Mehta and I wrote a series of papers which occupied us for several years and we were able to go a lot further. The most interesting thing that came out of that was in effect a sort of a general classification of all the possible ensembles. Whereas Wigner had just chosen one arbitrarily, we were able to prove that there are in fact precisely three irreducible ensembles in a well-defined mathematical sense; that every possible matrix ensemble with certain properties of invariance is a direct product of irreducible components, and each irreducible component then has to be one of three types. And the three types are what we call orthogonal, unitary and simplectic. And so the orthogonal one is where it is time reversal invariant and integer spin; and the unitary one is where there's no time reversal invariance; and the simplectic is where it's time reversal invariant with half integer spin. And so those are the only three possibilities, and they have very different behaviour as far as the level spacing distributions are concerned. You have always, in all three cases, you have a repulsion between nearest neighbour levels, so they're not randomly distributed, and a strong level repulsion is different in the three cases. It's weakest in the orthogonal case, and then a little bit stronger in the unitary case, and strongest of all in the simplectic case. So we were able to develop this theory of random matrices into a much more general form and also to prove a lot more fundamental properties of the spacing distributions.

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: Institute of Advanced Study, Princeton University, Madan Lal Mehta

Duration: 2 minutes, 13 seconds

Date story recorded: June 1998

Date story went live: 24 January 2008