Unconventional decay law for excited states in closed many-body systems

We study the time evolution of an initially excited many-body state in a finite system of interacting Fermi particles in the situation when the interaction gives rise to the "chaotic" structure of compound states. This situation is generic for highly excited many-particle states in quantum systems such as heavy nuclei, complex atoms, quantum dots, spin systems, and quantum computers. For a strong interaction the leading term for the return probability W(t) has the form W(t) approximately exp(-Delta(2)(E)t(2)) with Delta(2)(E) as the variance of the strength function. The conventional exponential linear dependence W(t)=C exp(-Gammat) formally arises for a very larger time. However, the prefactor C turns out to be exponentially large, thus resulting in a strong difference from the conventional estimate for W(t).