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Interacting many-particle systems with a mean-field one body part plus achaos generating random two-body interaction having strength $\lambda$, exhibitPoisson to GOE and Breit-Wigner (BW) to Gaussian transitions in levelfluctuations and strength functions with transition points marked by$\lambda=\lambda_c$ and $\lambda=\lambda_F$, respectively; $\lambda_F >>\lambda_c$. For these systems theory for matrix elements of one-body transitionoperators is available, as valid in the Gaussian domain, with $\lambda >\lambda_F$, in terms of orbitals occupation numbers, level densities and anintegral involving a bivariate Gaussian in the initial and final energies. Herewe show that, using bivariate $t$-distribution, the theory extends below fromthe Gaussian regime to the BW regime up to $\lambda=\lambda_c$. This is welltested in numerical calculations for six spinless fermions in twelve singleparticle states.Comment: 7 pages, 2 figure

physical review. e, statistical, nonlinear and soft matter physics

Bivariate-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>t</mml:mi></mml:math>distribution for transition matrix elements in Breit-Wigner to Gaussian domains of interacting particle systems

Bivariate-tdistribution for transition matrix elements in Breit-Wigner to Gaussian domains of interacting particle systems