Wigner surmise

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In mathematical physics, the Wigner surmise is a statement about the probability distribution of the spaces between points in the spectra of nuclei of heavy atoms, which have many degrees of freedom, or quantum systems with few degrees of freedom but chaotic classical dynamics. It was proposed by Eugene Wigner in probability theory.[1] The surmise was a result of Wigner's introduction of random matrices in the field of nuclear physics. The surmise consists of two postulates:

Here, where S is a particular spacing and D is the mean distance between neighboring intervals.[2]
  • In a mixed sequence (spin and parity are different), the probability density function can be obtained by randomly superimposing simple sequences.

The above result is exact for real symmetric matrices , with elements that are independent standard gaussian random variables, with joint distribution proportional to

In practice, it is a good approximation for the actual distribution for real symmetric matrices of any dimension. The corresponding result for complex hermitian matrices (which is also exact in the case and a good approximation in general) with distribution proportional to , is given by

See also[edit]


  1. ^ Mehta, Madan Lal (6 October 2004). Random Matrices By Madan Lal Mehta. p. 13. ISBN 9780080474113.
  2. ^ Benenti, Giuliano; Casati, Giulio; Strini, Giuliano (2004). Principles of Quantum Computation and Information. p. 406. ISBN 9789812563453.