Statistical properties of the eigenvalue motion of Hermitian matrices

Abstract

It is noted that the t→∞ distribution for the eigenvalues of the Hermitian matrix H0+tV as given by Yukawa [Phys. Lett. A 116 (1986) 227] is identical to a solvable distribution first discussed by Gaudin [Nucl. Phys. 25 (1962) 447]. A new method of calculating the n-particle distribution function is presented. The probability that an interval of length s is free of eigenvalues, which is given exactly by a Fredholm determinant, is analysed in the small and large s limits. © 1993.