In this talk I will give a brief introduction to the density-matrix renormalization group method, which has allowed the calculation of static properties in 1D strongly correlated quantum systems with unprecedented precision. I will then explain how this method can be extended to calculate the dynamics of pure and mixed quantum states also far from equilibrium. This new method and its potential will be illustrated by applications in the field of far-from-equilibrium magnetization dynamics and the possible observation of spin-charge separation in ultracold fermionic gases in optical lattices.

Aachen