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@ARTICLE{Belitsky:865027,
      author       = {Belitsky, V. and Schütz, G. M.},
      title        = {{D}uality, supersymmetry and non-conservative random walks},
      journal      = {Journal of statistical mechanics: theory and experiment},
      volume       = {2019},
      number       = {5},
      issn         = {1742-5468},
      address      = {Bristol},
      publisher    = {IOP Publ.},
      reportid     = {FZJ-2019-04592},
      pages        = {054004},
      year         = {2019},
      abstract     = {We derive a probabilistic interpretation of the observation
                      that the quantum XY chain is supersymmetric in the sense
                      that the Hamiltonian commutes with the generators of a
                      subalgebra of the universal enveloping algebra of the Lie
                      superalgebra and its deformations. The XY chain is shown to
                      be the generator of a Markov process that describes
                      classical vicious random walkers that annihilate immediately
                      when they arrive on the same site, while new random walkers
                      are created at neighbouring sites. The supersymmetry leads
                      to a probabilistic self-duality relation and a duality
                      between the random walk model with an even and odd number of
                      particles, respectively.},
      cin          = {ICS-2},
      ddc          = {530},
      cid          = {I:(DE-Juel1)ICS-2-20110106},
      pnm          = {551 - Functional Macromolecules and Complexes (POF3-551)},
      pid          = {G:(DE-HGF)POF3-551},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000468501000001},
      doi          = {10.1088/1742-5468/ab14d6},
      url          = {https://juser.fz-juelich.de/record/865027},
}