This 'Momentum' research group, financed by the HAS and the BME, studies the dynamics of one-dimensional quantum systems, such as spin chains, one-dimensional Bose gases, and related quantum field theory models. Compared to higher dimensional systems, quantum effects and correlations between degrees of freedom play a much more important role in one dimension, resulting in numerous exotic phenomena. In a significant part of these phenomena the so-called integrability or its absence play a central role.