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The multi-electron dynamics during the tunnel ionization of a correlated quantumsystem is investigated by comparison of the solution of the time-dependent Schr\"odinger equation (TDSE) with the time-dependent configuration interaction singles approach (TDCIS). Thereby, we point out the relevance of a multi-electron description of the tunnel ionization process especially for weakly confined quantum systems i.e. for instance poly-atomic molecules or semiconductor quantum dots. Within this context, we observe that adiabatic driving by an intense light field can even enhance the correlations between still trapped electrons.
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