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In many--body and other systems, the physics situation often allows one tointerpret certain, distinct states by means of a simple picture. In thisinterpretation, the distinct states are not eigenstates of the fullHamiltonian. Hence, there is an interaction which makes the distinct states actas doorways into background states which are modeled statistically. The crucialquantities are the overlaps between the eigenstates of the full Hamiltonian andthe doorway states, that is, the coupling coefficients occuring in theexpansion of true eigenstates in the simple model basis. Recently, thedistribution of the maximum coupling coefficients was introduced as a new,highly sensitive statistical observable. In the particularly important regimeof weak interactions, this distribution is very well approximated by thefidelity distribution, defined as the distribution of the overlap between thedoorway states with interaction and without interaction. Using a random matrixmodel, we calculate the latter distribution exactly for regular and chaoticbackground states in the cases of preserved and fully broken time--reversalinvariance. We also perform numerical simulations and find excellent agreementwith our analytical results.

Exact Coupling Coefficient Distribution in the Doorway Mechanism