Description of Quantum Systems by Random Matrix Ensembles of High Dimensions: ICSSUR’6 Poster Session

The new Theorem on location of maximum of probability density functions of dimensionless second difference of the three adjacent energy levels for N -dimensional Gaussian orthogonal ensemble GOE(N), N -dimensional Gaussian unitary ensemble GUE(N), N -dimensional Gaussian symplectic ensemble GSE(N), and Poisson ensemble PE, is formulated: The probability density functions of the dimensionless second difference of the three adjacent energy levels take on maximum at the origin for the following ensembles: GOE(N), GUE(N), GSE(N), and PE, where N ≥ 3. The notions of level homogenization with level clustering and level homogenization with level repulsion are introduced.