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Investigation of complex-energy shift in time-dependent perturbed decaying systems

In this paper a wavefunction-centered description of decaying states that are coupled to an external potential of general time-dependence is investigated. We present the application of non-Hermitian spectral calculations merged with the (t, t′)-formalism to estimate the possible time-dependent potential induced corrections to the lifetime of quasi-stationary states. The appliance of the formalism is demonstrated on some specific potential models as illustrative examples that represent decaying systems. We argue, that the presented framework and computational technique might provide a way to evaluate the lifetime of quasi-stationary states of different types of physical decaying systems that are subjected to perturbative, time-dependent drivings.