BGS conjecture
The Bohigas–Giannoni–Schmit (BGS) conjecture also known as the random matrix conjecture) for simple quantum mechanical systems (ergodic with a classical limit) few degrees of freedom holds that spectra of time reversal-invariant systems whose classical analogues are K-systems show the same fluctuation properties as predicted by the GOE (Gaussian orthogonal ensembles). Alternatively, the spectral fluctuation measures of a classically chaotic quantum system coincide with those of the canonical random-matrix ensemble in the same symmetry class (unitary, orthogonal, or symplectic).