Bivariate averaging and the Wigner distribution function

V. N. Gorshenkov, V. L. Kon'kov

Fan, Hong-Yi, Wang +1 more

Fan Hong-Yi, Wang Tong-Tong

We introduce a kind of generalized Wigner operator, whose normally ordered form can lead to the bivariate normal distribution in p-q phase space. While this bivariate normal distribution corresponds to the pure vacuum state in the generalized Wigner function phase space, it corresponds to a mixed state in the usual Wigner function phase space.

GERALD J. IAFRATE, H. L. Grubin, David K. Ferry

Gen-ichi Hatakoshi

V. K. B. Kota, N. D. Chavda, R. Sahu

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.