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@ARTICLE{Wuttke:153823,
      author       = {Wuttke, Joachim},
      title        = {{T}he zig-zag walk with scattering and absorption on the
                      real half line and in a lattice model},
      journal      = {Journal of physics / A},
      volume       = {47},
      number       = {21},
      issn         = {1751-8121},
      address      = {Bristol},
      publisher    = {IOP Publ.},
      reportid     = {FZJ-2014-03303},
      pages        = {215203 -},
      year         = {2014},
      abstract     = {The Darwin?Hamilton equations, describing one-dimensional
                      transport with scattering and absorption, are expanded into
                      a recursion. The solution involves ballot numbers. The
                      recurrence probability as function of scattering order is
                      given by Catalan numbers. To reproduce this analytical
                      result in a lattice model, a novel relation between Narayana
                      and Catalan numbers is derived.},
      cin          = {Neutronenstreuung ; JCNS-1 / JCNS (München) ; Jülich
                      Centre for Neutron Science JCNS (München) ; JCNS-FRM-II /
                      JCNS-2},
      ddc          = {530},
      cid          = {I:(DE-Juel1)JCNS-1-20110106 /
                      I:(DE-Juel1)JCNS-FRM-II-20110218 /
                      I:(DE-Juel1)JCNS-2-20110106},
      pnm          = {451 - Soft Matter Composites (POF2-451) / 54G - JCNS
                      (POF2-54G24) / 422 - Spin-based and quantum information
                      (POF2-422) / 424 - Exploratory materials and phenomena
                      (POF2-424) / 542 - Neutrons (POF2-542) / 544 - In-house
                      Research with PNI (POF2-544)},
      pid          = {G:(DE-HGF)POF2-451 / G:(DE-HGF)POF2-54G24 /
                      G:(DE-HGF)POF2-422 / G:(DE-HGF)POF2-424 / G:(DE-HGF)POF2-542
                      / G:(DE-HGF)POF2-544},
      experiment   = {EXP:(DE-MLZ)NOSPEC-20140101},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000336718700008},
      doi          = {10.1088/1751-8113/47/21/215203},
      url          = {https://juser.fz-juelich.de/record/153823},
}