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.
Department of Physics, Indian Institute of Technology, Kharagpur, India.
Pragya
P
Shukla