Eigenfunction statistics of complex systems: a common mathematical formulation.
We derive a common mathematical formulation for the eigenfunction statistics of Hermitian operators, represented by a multiparametric probability density. The system information in the formulation enters through two parameters only, namely, system size and the complexity parameter, a function of all system parameters including size. The behavior is contrary to the eigenvalue statistics which is sensitive to the complexity parameter only and shows a single parametric scaling. The existence of a mathematical formulation of both eigenfunctions and eigenvalues common to a wide range of complex systems indicates the possibility of a similar formulation for many physical properties. This also suggests the possibility to classify them in various universality classes defined by the complexity parameter.
Shukla
Pragya
P
Department of Physics, Indian Institute of Technology, Kharagpur, India.