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

Details Bivariate $t$-distribution for transition matrix elements in Breit-Wigner to Gaussian domains of interacting particle systems Bivariate $t$-distribution for transition matrix elements in Breit-Wigner to Gaussian domains of interacting particle systems

2005-08-17

arxiv.org/abs/nlin/0508023v1

Nonlinear Sciences

Chaotic Dynamics

7 pages, 2 figures

Scientific paper

10.1103/PhysRevE.73.047203

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 GOE 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 theory for matrix elements of one-body transition operators is available, as valid in the Gaussian domain, with $\lambda > \lambda_F$, in terms of orbitals occupation numbers, level densities and an integral involving a bivariate Gaussian in the initial and final energies. Here we show that, using 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 six spinless fermions in twelve single particle states.

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