3,625 research outputs found
Anderson localization in generalized discrete time quantum walks
We study Anderson localization in a generalized discrete time quantum walk -
a unitary map related to a Floquet driven quantum lattice. It is controlled by
a quantum coin matrix which depends on four angles with the meaning of
potential and kinetic energy, and external and internal synthetic flux. Such
quantum coins can be engineered with microwave pulses in qubit chains. The
ordered case yields a two-band eigenvalue structure on the unit circle which
becomes completely flat in the limit of vanishing kinetic energy. Disorder in
the external magnetic field does not impact localization. Disorder in all the
remaining angles yields Anderson localization. In particular, kinetic energy
disorder leads to logarithmic divergence of the localization length at spectral
symmetry points. Strong disorder in potential and internal magnetic field
energies allows to obtain analytical expressions for spectrally independent
localization length which is highly useful for various applications.Comment: 11 pages, 14 figure
Graph Metrics for Temporal Networks
Temporal networks, i.e., networks in which the interactions among a set of
elementary units change over time, can be modelled in terms of time-varying
graphs, which are time-ordered sequences of graphs over a set of nodes. In such
graphs, the concepts of node adjacency and reachability crucially depend on the
exact temporal ordering of the links. Consequently, all the concepts and
metrics proposed and used for the characterisation of static complex networks
have to be redefined or appropriately extended to time-varying graphs, in order
to take into account the effects of time ordering on causality. In this chapter
we discuss how to represent temporal networks and we review the definitions of
walks, paths, connectedness and connected components valid for graphs in which
the links fluctuate over time. We then focus on temporal node-node distance,
and we discuss how to characterise link persistence and the temporal
small-world behaviour in this class of networks. Finally, we discuss the
extension of classic centrality measures, including closeness, betweenness and
spectral centrality, to the case of time-varying graphs, and we review the work
on temporal motifs analysis and the definition of modularity for temporal
graphs.Comment: 26 pages, 5 figures, Chapter in Temporal Networks (Petter Holme and
Jari Saram\"aki editors). Springer. Berlin, Heidelberg 201
Random Walks Estimate Land Value
Expected urban population doubling calls for a compelling theory of the city.
Random walks and diffusions defined on spatial city graphs spot hidden areas of
geographical isolation in the urban landscape going downhill. First--passage
time to a place correlates with assessed value of land in that. The method
accounting the average number of random turns at junctions on the way to reach
any particular place in the city from various starting points could be used to
identify isolated neighborhoods in big cities with a complex web of roads,
walkways and public transport systems
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