Random-matrix theory and complex atomic spectra

Around 1950, Wigner introduced the idea of modelling physical reality with an ensemble of random matrices while studying the energy levels of heavy atomic nuclei. Since then, the field of random-matrix theory has grown tremendously, with applications ranging from fluctuations on the economic markets to complex atomic spectra. The purpose of this short article is to review several attempts to apply the basic concepts of random-matrix theory to the structure and radiative transitions of atoms and ions, using the random matrices originally introduced by Wigner in the framework of the gaussian orthogonal ensemble. Some intrinsic properties of complex-atom physics, which could be enlightened by random-matrix theory, are presented.