Decoherence models for discrete-time quantum walks and their application to neutral atom experiments

We discuss decoherence in discrete-time quantum walks in terms of a phenomenological model that distinguishes spin and spatial decoherence. We identify the dominating mechanisms that affect quantum-walk experiments realized with neutral atoms walking in an optical lattice. From the measured spatial distributions, we determine with good precision the amount of decoherence per step, which provides a quantitative indication of the quality of our quantum walks. In particular, we find that spin decoherence is the main mechanism responsible for the loss of coherence in our experiment. We also find that the sole observation of ballistic-instead of diffusive-expansion in position space is not a good indicator of the range of coherent delocalization. We provide further physical insight by distinguishing the effects of short- and long-time spin dephasing mechanisms. We introduce the concept of coherence length in the discrete-time quantum walk, which quantifies the range of spatial coherences. Unexpectedly, we find that quasi-stationary dephasing does not modify the local properties of the quantum walk, but instead affects spatial coherences. For a visual representation of decoherence phenomena in phase space, we have developed a formalism based on a discrete analogue of the Wigner function. We show that the effects of spin and spatial decoherence differ dramatically in momentum space.

Do Children's Health Resources Differ According to Preschool Physical Activity Programmes and Parental Behaviour? A Mixed Methods Study

Preschool can have positive effects on the development of a healthy lifestyle. The present study analysed to what extent different conditions, structures and behavioural models in preschool and family-children's central social microsystems-can lead to differences in children's health resources. Using a cross-sectional mixed methods approach, contrast analyses of "preschools with systematic physical activity programmes" versus "preschools without physical activity programmes" were conducted to assess the extent to which children's physical activity, quality of life and social behaviour differ between preschools with systematic and preschools without physical activity programmes. Differences in children's physical activity according to parental behaviour were likewise assessed. Data on child-related outcomes and parent-related factors were collected via parent questionnaires and child interviews. A qualitative focused ethnographic study was performed to obtain deeper insight into the quantitative survey data. Two hundred and twenty seven (227) children were interviewed at 21 preschools with systematic physical activity programmes, and 190 at 25 preschools without physical activity programmes. There was no significant difference in children's physical activity levels between the two preschool types (p = 0.709). However, the qualitative data showed differences in the design and quality of programmes to promote children's physical activity. Data triangulation revealed a strong influence of parental behaviour. The triangulation of methods provided comprehensive insight into the nature and extent of physical activity programmes in preschools and made it possible to capture the associations between systematic physical activity promotion and children's health resources in a differential manner.