title: Bivariate- distribution for transition matrix elements in Breit-Wigner to Gaussian domains of interacting particle systems.
abstract: Interacting many-particle systems with a mean-field one-body part plus a chaos generating random two-body interaction having strength lambda exhibit Poisson to Gaussian orthogonal ensemble and Breit-Wigner (BW) to Gaussian transitions in level fluctuations and strength functions with transition points marked by lambda = lambda c and lambda = lambda F, respectively; lambda F >> lambda c. For these systems a theory for the matrix elements of one-body transition operators is available, as valid in the Gaussian domain, with lambda > lambda F, in terms of orbital occupation numbers, level densities, and an integral involving a bivariate Gaussian in the initial and final energies. Here we show that, using a bivariate-t distribution, the theory extends below from the Gaussian regime to the BW regime up to lambda = lambda c. This is well tested in numerical calculations for 6 spinless fermions in 12 single-particle states.
authors.affiliation: Physical Research Laboratory, Ahmedabad 380 009, India.
authors.forename: V K B
authors.initials: VK
authors.lastname: Kota
authors.forename: N D
authors.initials: ND
authors.lastname: Chavda
authors.forename: R
authors.initials: R
authors.lastname: Sahu