  The Gaussian Orthogonal Ensemble (GOE) of random matrices has been widely
employed to describe diverse phenomena in strongly coupled quantum systems. An
important prediction is that the decay rates of the GOE eigenstates fluctuate
according to the distribution for one degree of freedom, as derived by Brink
and by Porter and Thomas. However, we find that the coupling to the decay
channels can change the effective number of degrees of freedom from $\nu = 1$
to $\nu = 2$. Our conclusions are based on a configuration-interaction
Hamiltonian originally constructed to test the validity of transition-state
theory, also known as Rice-Ramsperger-Kassel-Marcus (RRKM) theory in chemistry.
The internal Hamiltonian consists of two sets of GOE reservoirs connected by an
internal channel. We find that the effective number of degrees of freedom $\nu$
can vary from one to two depending on the control parameter $\rho \Gamma$,
where $\rho$ is the level density in the first reservoir and $\Gamma$ is the
level decay width. The $\nu = 2$ distribution is a well-known property of the
Gaussian Unitary ensemble (GUE); our model demonstrates that the GUE
fluctuations can be present under much milder conditions. Our treatment of the
model permits an analytic derivation for $\rho\Gamma \gtrsim 1$.
