Strongly trapped two-dimensional quantum walks

Discrete time quantum walks (DTQWs) are nontrivial generalizations of random walks with a broad scope of applications. In particular, they can be used as computational primitives, and they are suitable tools for simulating other quantum systems. DTQWs usually spread ballistically due to their quantumness. In some cases, however, they can remain localized at their initial state (trapping). The trapping and other fundamental properties of DTQWs are determined by the choice of the coin operator. We introduce and analyze an up to now uncharted type of walks driven by a coin class leading to strong trapping, complementing the known list of walks. This class of walks exhibit a number of exciting properties with the possible applications ranging from light pulse trapping in a medium to topological effects and quantum search.Comment: 5 pages, 4 figures, Accepted for publication in Physical Review

Binding of Oxovanadium(IV) Complexes to Blood Serum Albumins

In this work the binding of VIVO2+ and VIVO-complexes to serum albumins {human serum albumin (HSA), bovine serum albumin (BSA) and porcine serum albumin (PSA)} are studied using circular dichroism (CD), electron paramagnetic resonance (EPR) and visible absorption spectroscopy. The results confirm previous findings that VIVO2+ occupies at least two types of binding sites on albumin: ‘the strong vanadium binding site’ (designated by VBS1) and ‘the weak vanadium binding sites’ (designated by VBS2). VBS1 binds 1 mol equivalent of VIVO2+. On the other hand VBS2 correspond to binding of several mol equivalents of VIVO, and studies done with PSA in the presence of excess ZnII ions indicate that VSB2 corresponds to two distinct types of sites. The hyperfine coupling constant Az for VIVO2+ binding at VBS2 on HSA and BSA are all very similar (~168 × 10-4 cm-1) but differ slightly on PSA (~166 × 10-4 cm-1) due to differences in the binding sets. When (VIVO)-HSA systems are titrated with maltol ternary species of (maltol)m(VIVO)mHSA and (maltol)2m(VIVO)mHSA stoichiometry form which are clearly distinguishable from the binary (VIVO)-HSA system by the type and intensity of the CD spectra recorded. Changes are also observable in the intensity of the X-band EPR spectra, but not much in the hyperfine coupling constants Az, which are all in the range 166-167 × 10-4 cm-1. The results further demonstrate that the presence of maltol may enhance the binding of VIVO to albumin

Discrete time quantum walks on percolation graphs

Randomly breaking connections in a graph alters its transport properties, a model used to describe percolation. In the case of quantum walks, dynamic percolation graphs represent a special type of imperfections, where the connections appear and disappear randomly in each step during the time evolution. The resulting open system dynamics is hard to treat numerically in general. We shortly review the literature on this problem. We then present our method to solve the evolution on finite percolation graphs in the long time limit, applying the asymptotic methods concerning random unitary maps. We work out the case of one dimensional chains in detail and provide a concrete, step by step numerical example in order to give more insight into the possible asymptotic behavior. The results about the case of the two-dimensional integer lattice are summarized, focusing on the Grover type coin operator.Comment: 22 pages, 3 figure