SURVIVAL AMPLITUDE, INSTANTANEOUS ENERGY AND DECAY RATE OF AN UNSTABLE SYSTEM: ANALYTICAL RESULTS.

We consider a model of an unstable state defined by the truncated Breit-Wigner energy density distribution function. An analytical form of the survival amplitude a(t) of the state considered is found. Our attention is focused on the late time properties of a(t) and on effects generated by the non-exponential behavior of this amplitude in the late time region: In 1957, Khalfin proved that this amplitude tends to zero as t goes to the infinity more slowly than any exponential function of t. This effect can be described using a time-dependent decay rate γ(t), and then the Khalfin result means that this γ(t) is not a constant but at late times, it tends to zero as t goes to the infinity. It appears that the energy E(t) of the unstable state behaves similarly: It tends to the minimal energy Emin of the system as t → ∞. Within the model considered, we find two first leading time-dependent elements of late time asymptotic expansions of E(t) and γ(t). We discuss also possible implications of such a late time asymptotic properties of E(t) and (t) and cases where these properties may manifest themselves. [ABSTRACT FROM AUTHOR]