caa a22 4500 445864923 CHVBK 20180317145455.0 cr unu---uuuuu 170323e20110901xx s 000 0 eng 10.1140/epjd/e2011-20138-8 doi (NATIONALLICENCE)springer-10.1140/epjd/e2011-20138-8 Quantum walk with jumps [Elektronische Daten] [H. Lavička, V. Potoček, T. Kiss, E. Lutz, I. Jex] Abstract.: We analyze a special class of 1-D quantum walks (QWs) realized using optical multi-ports. We assume non-perfect multi-ports showing errors in the connectivity, i.e. with a small probability the multi-ports can connect not to their nearest neighbor but to another multi-port at a fixed distance - we call this a jump. We study two cases of QW with jumps where multiple displacements can emerge at one timestep. The first case assumes time-correlated jumps (static disorder). In the second case, we choose the positions of jumps randomly in time (dynamic disorder). The probability distributions of position of the QW walker in both instances differ significantly: dynamic disorder leads to a Gaussian-like distribution, while for static disorder we find two distinct behaviors depending on the parity of jump size. In the case of even-sized jumps, the distribution exhibits a three-peak profile around the position of the initial excitation, whereas the probability distribution in the odd case follows a Laplace-like discrete distribution modulated by additional (exponential) peaks for long times. Finally, our numerical results indicate that by an appropriate mapping a universal functional behavior of the variance of the long-time probability distribution can be revealed with respect to the scaled average of jump size. EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg, 2011 Lavička H. Czech Technical University in Prague, Faculty of Nuclear Sciences and Physical Engineering, Department of Physics, Břehová7, 115 19, Praha 1, Czech Republic aut Potoček V. Czech Technical University in Prague, Faculty of Nuclear Sciences and Physical Engineering, Department of Physics, Břehová7, 115 19, Praha 1, Czech Republic aut Kiss T. Research Institute for Solid State Physics and Optics, Hungarian Academy of Sciences, P.O. Box 49, 1525, Budapest, Hungary aut Lutz E. Department of Physics, University of Augsburg, 86135, Augsburg, Germany aut Jex I. Czech Technical University in Prague, Faculty of Nuclear Sciences and Physical Engineering, Department of Physics, Břehová7, 115 19, Praha 1, Czech Republic aut The European Physical Journal D Springer-Verlag 64/1(2011-09-01), 119-129 1434-6060 64:1<119 2011 64 10053 https://doi.org/10.1140/epjd/e2011-20138-8 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1140/epjd/e2011-20138-8 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Lavička H. Czech Technical University in Prague, Faculty of Nuclear Sciences and Physical Engineering, Department of Physics, Břehová7, 115 19, Praha 1, Czech Republic aut NATIONALLICENCE 700 1- Potoček V. Czech Technical University in Prague, Faculty of Nuclear Sciences and Physical Engineering, Department of Physics, Břehová7, 115 19, Praha 1, Czech Republic aut NATIONALLICENCE 700 1- Kiss T. Research Institute for Solid State Physics and Optics, Hungarian Academy of Sciences, P.O. Box 49, 1525, Budapest, Hungary aut NATIONALLICENCE 700 1- Lutz E. Department of Physics, University of Augsburg, 86135, Augsburg, Germany aut NATIONALLICENCE 700 1- Jex I. Czech Technical University in Prague, Faculty of Nuclear Sciences and Physical Engineering, Department of Physics, Břehová7, 115 19, Praha 1, Czech Republic aut NATIONALLICENCE 773 0- The European Physical Journal D Springer-Verlag 64/1(2011-09-01), 119-129 1434-6060 64:1<119 2011 64 10053 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer