Survival probability of a local excitation in a non-Markovian environment: Return effects and Survival collapse

E. RUFEIL FIORI; H. M. PASTAWSKI

Trieste

Congreso; College on Physics of Nano-Devices; 2006

Abdus Salam International Centre for Theoretical Physics

Nanosystems are never isolated, but they interact with the macroscopic world. In consequence the excitations have a survival probability Poo(t) which typically decay according to the Fermi Golden Rule. However, this approximation neglects memory effects in the environment, which could be relevant. In this work we address effects that an electrode, considered as "environment", has on the excitations of a quantum dot. To simplify the treatment we consider a single state of the dot which is weakly coupled to an environment whose dynamics can be solved within a Hamiltonian model. Various works on models for nuclei, composite particles and excited atoms in a free electromagnetic field, showed that the exponential decay has superimposed beats and does not hold for very short and very long times, compared with the lifetime of the system. In Ref. [RP05] we presented a model describing the evolution of a surface excitation in a semi-infinite spin chain, a model that is solved analytically and susceptible for an experimental test. Here, we present a general analysis showing the quantum nature of the deviations from the Fermi Golden Rule. We identify three time regimes in the decay of the survival probability Poo(t): (1) For short times the decay is quadratic, as is expected when the coupling of the local state with the continuum is perturbative and for non-divergent Hamiltonian second moment. This lasts for a time proportional to the spectral density of the final states evaluated at the decaying state energy, (2) An intermediate regime characterized by an exponential behavior, the self-consistent Fermi Golden Rule (SC-FGR), where the rate, the pre-exponential factor and the characteristic frequency are found self-consistently. (3) At long-times, t>t_{R}, the exponential decay of the pure survival probability is overrun by an inverse power law, which is identified with the return probability enabled by the slow quantum diffusion in the environment. At this last cross-over time, quantum interference could lead to a dip in Poo(t) of several orders of magnitude. This survival collapse, which last for a brief period, is identified with a destructive interference between the pure survival amplitude, i.e., the SC-FGR component, and the return amplitude, associated with high orders in a perturbation theory. The identification of these regimes is very important to assess the validity of the Markovian approximation and to describe memory effects of the environment surrounding the nanodevices.