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@ARTICLE{Popkov:20484,
      author       = {Popkov, V. and Salerno, M. and Schütz, G.M.},
      title        = {{B}ehavior of magnetic currents in anisotropic {H}eisenberg
                      spin chains out of equilibrium},
      journal      = {Physical review / E},
      volume       = {85},
      number       = {3},
      issn         = {1539-3755},
      address      = {College Park, Md.},
      publisher    = {APS},
      reportid     = {PreJuSER-20484},
      pages        = {031137},
      year         = {2012},
      note         = {V.P. acknowledges the University of Salerno for a research
                      grant to support this work. M. S. acknowledges support from
                      the Ministero dell' Istruzione, dell' Universita e della
                      Ricerca (MIUR) through a Programma di Ricerca Scientifica di
                      Rilevante Interesse Nazionale (PRIN) initiative.},
      abstract     = {The behavior of the magnetic currents in one-dimensional
                      Heisenberg XXZ spin chains kept out of equilibrium by
                      boundary driving fields is investigated. In particular, the
                      dependence of the spin currents on the anisotropy parameter
                      Delta and on the boundary fields is studied both
                      analytically and numerically in the framework of the
                      Lindblad master equation formalism. We show that the spin
                      current can be maximized with appropriate choices of the
                      boundary fields, and for odd system sizes, N, we demonstrate
                      the existence of additional symmetries that cause the
                      current to be an odd function of Delta. From direct
                      numerical integrations of the quantum master equation, we
                      find that for an arbitrary N the current J(z)(N) vanishes
                      for Delta = 0, while for Delta negative it alternates its
                      sign with the system size. In the gapless critical region
                      |Delta| < 1, the scaling of the current is shown to be
                      J(z)(N) similar to 1/N while in the gapped region |Delta| >
                      1 we find that J(z) (N) similar to exp(-alpha N). A simple
                      mean-field approach, which predicts rather well the values
                      of J(z) (N) for the gapped region and the values of the
                      absolute current maxima in the critical region, is
                      developed. The existence of two different stationary
                      solutions for the mean-field density matrix in the whole
                      parameter range is also demonstrated.},
      keywords     = {J (WoSType)},
      cin          = {ICS-2},
      ddc          = {530},
      cid          = {I:(DE-Juel1)ICS-2-20110106},
      pnm          = {BioSoft: Makromolekulare Systeme und biologische
                      Informationsverarbeitung},
      pid          = {G:(DE-Juel1)FUEK505},
      shelfmark    = {Physics, Fluids $\&$ Plasmas / Physics, Mathematical},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000301849600004},
      doi          = {10.1103/PhysRevE.85.031137},
      url          = {https://juser.fz-juelich.de/record/20484},
}