We introduce quantum walks with a time-dependent coin, and show how they include, as a particular case, the generalized quantum walk recently studied by Wojcik et al. [Phys. Rev. Lett. 93, 180601(2004)] which exhibits interesting dynamical localization and quasiperiodic dynamics. Our proposal allows for a much easier implementation of this particular rich dynamics than the original one. Moreover, it allows for an additional control on the walk, which can be used to compensate for phases appearing due to external interactions. To illustrate its feasibility, we discuss an example using an optical cavity. We also derive an approximated solution in the continuous limit (long-wavelength approximation) which provides physical insight about the process.

1 SCA40 (0.1 nM-0.1 mM) produced concentration-dependent suppression of the spontaneous tone of human isolated bronchus (-log EC5 = 6.85 + 0.09; n = 10) and reached a maximal relaxation similar to that of theophylline (3 mM). The potency (-log EC50 values) of SCA40 compared to other relaxants was rolipram (7.44 + 0.12; n = 9) > SCA40 > levcromakalim (6.49 + 0.04; n = 6) > SKF94120 (5.87 + 0.10; n = 9). 2 When tested against the activity of the isoenzymes of cyclic nucleotide phosphodiesterase (PDE) isolated from human bronchus, SCA40 proved highly potent against PDE III (-log IC50 = 6.47 + 0.16; n=4). It was markedly less potent against PDE IV (4.82+0.18; n=4) and PDE V (4.32+0.11; n=4). 3 Human polymorphonuclear leukocytes (PMNs) stimulated with N-formylmethionyl-leucyl-phenylalanine (FMLP) produced a concentration-dependent superoxide anion generation and elastase release. SCA40(1 nM-10 /M) produced a concentration-related inhibition of FMLP (30 nM EC50)-induced superoxide production (-log IC50 = 5.48 + 0.10; n = 6) and elastase release (-log IC50 = 5.50 + 0.26; n=6). Rolipram was an effective inhibitor of superoxide generation and elastase release (-log IC50 values -8) while SKF94120 and levcromakalim were scarcely effective.4 FMLP (30 nM) and thimerosal (20 pM) induced leukotriene B4 production and elevation of intracellular calcium concentration in human PMNs. The production of leukotriene B4 was inhibited by SCA40 in a concentration-related manner (-log IC50 = 5.94 + 0.22; n = 6) but SCA40 was less effective against the elevation of intracellular calcium. Rolipram was an effective inhibitor of leukotriene B4 synthesis (-log IC50 -7) and intracellular calcium elevation (-log IC50 -6) while SKF94120 and levcromakalim were scarcely effective. 5 It is concluded that SCA40 is an effective inhibitor of the inherent tone of human isolated bronchus. The bronchodilatation produced by SCA40 appears mainly related to PDE inhibition since the potency of SCA40 as a relaxant of human isolated bronchus was found to be close to its potency as inhibitor of PDE III activity isolated from human bronchus. In addition, SCA40 exhibited inhibitory effects on human PMN function stimulated by FMLP. These effects may be related to the ability of SCA40 to inhibit PDE IV from human PMNs while the contribution of PDE V inhibition is uncertain. We found no evidence of a role for levcromakalim-sensitive plasmalemmal K+-channels in human PMNs.

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