Generally, the addition or removal of a single particle in a many-body system does not correspond to an exact eigenstate of the system. Thus the resulting coherent excitation evolves in time. As discussed here, the evolution at short times upon the excitation with the energy ε exhibits a quadratic decay [with the rate constant σ2(ε)]. Later on, after some time τ(ε), the exponential decay sets in. It is governed by another rate constant γ(ε). This behavior is generic for many realistic finite and extended systems. For a finite system it is possible to assess this behavior full numerically using an exact solution of the many-body problem. We present a simple model for the electron spectral function that links together all three aforementioned parameters and give a prescription for how the energy uncertainty σ2(ε) can be computed within the many-body perturbation theory. Our numerical results demonstrate that the model approach accurately reproduces the exact spectral function in a large range of energies even in the case of fragmented many-body states. We show that the central quantity of this study σ2(ε) can easily be computed exactly or from approximate theories and, hence, can be used for their validation. We also point out how the set in time can be tested by means of attosecond spectroscopy.

A. R. acknowledge financial support from the European Research Council Advanced GrantDYNamo (ERC-2010-AdG-Proposal No. 267374), Spanish Grants (FIS2011-65702 C02-01 and PIB2010US-00652), ACI-Promociona (ACI2009- 1036), Grupos Consolidado UPV/EHU del Gobierno Vasco (IT-319-07), and European Commission projects CRONOS (280879-2CRONOSCP-FP7) andTHEMA(FP7-NMP-2008-SMALL-2, 228539).

Peer Reviewed