| The computation of the dynamical evolution of driven quantum systems is a complicated problem although the underlying equations of motions are linear. We discuss the numerical solution of the Schrödinger equation with a time-dependent Hamilton operator using commutator-free exponential time-propagators. These propagators are constructed as products of exponentials of simple weighted sums of the Hamilton operator. Their advantage is that they strictly preserve unitarity, allow for straightforward implementation, and provide high efficiency also for large scale problems. We discuss the derivation and error analysis of high-order commutator-free exponential time-propagators in the context of the Magnus expansion, and illustrate their application with several examples including arrays of interacting spins and general multi-level systems. |
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