# How come random matrices can predict energy spectra of heavy atoms?

Some of the applications of random matrices is to find the spectra of heavy atoms in nuclear physics which are usually difficult to find otherwise.

How can starting from randomness of some kind, such as random matrices, lead to prediction of that sort?

Any idea why this work?

Random matrices are used in string theory too, may be some string theorist here can shed some light on this topic

Revo

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If you answer this question, you'll be famous. The reason that the normal distribution works so well for many applications is the central limit theorem ... a lot of small effects tend to add up to a normal distribution. Possibly, something similar is going on here. –  Peter Shor Aug 8 '11 at 1:10
I'm curious about what sort of algorithm uses random matrices to calculate spectral lines... –  Colin K Aug 8 '11 at 5:41
@Colin, it's not so much an algorithm, just an observation that the distribution of energy eigenvalues for many heavy nuclei happen to fall upon the distribution of eigenvalues of a certain class of random matrices (gaussian um... something (orthogonal, unitary, symplectic - I forget which) ensemble). While perhaps not physically satisfying, I think Peter's comment is the best answer to this question. –  wsc Aug 8 '11 at 14:09
@wsc: It's not just heavy nuclei and random matrices; there are a number of other random processes which give rise to this same probability distribution of eigenvalues, and as far as I know, nobody has yet found a satisfactory explanation for why this happens. –  Peter Shor Aug 8 '11 at 14:29
@Revo: String theorists would be the last people to know why this happens; no knock on stringy guys, but deriving the properties of even light nuclei from just quarks and gluons is already an immensely heady task. (not to mention that calculating the spectra of heavy nuclei from nucleons and pions is also a difficult task, thus the immense beauty of their distribution being reproduced by the GUE.) –  wsc Aug 9 '11 at 3:27