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@ARTICLE{Jin:133045,
      author       = {Jin, Fengping and Michielsen, Kristel and Novotny, Mark A.
                      and Miyashita, Seiji and Yuan, Shengjun and De Raedt, Hans},
      title        = {{Q}uantum decoherence scaling with bath size: {I}mportance
                      of dynamics, connectivity, and randomness},
      journal      = {Physical review / A},
      volume       = {87},
      number       = {2},
      issn         = {1050-2947},
      address      = {College Park, Md.},
      publisher    = {APS},
      reportid     = {FZJ-2013-01609},
      pages        = {022117},
      year         = {2013},
      abstract     = {We consider the decoherence of a quantum system S coupled
                      to a quantum environment E. For states chosen uniformly at
                      random from the unit hypersphere in the Hilbert space of the
                      closed system S+E we derive a scaling relationship for the
                      sum of the off-diagonal elements of the reduced density
                      matrix of S as a function of the size DE of the Hilbert
                      space of E. This sum decreases as 1/√DE as long as DE≫1.
                      We test this scaling prediction by performing large-scale
                      simulations which solve the time-dependent Schrödinger
                      equation for a ring of spin-1/2 particles, four of them
                      belonging to S and the others to E, and for this ring with
                      small world bonds added in E and/or between S and E. The
                      spin-1/2 particles experience nearest-neighbor interactions
                      that are identical for the interactions within S and random
                      for the interactions within E and between S and E, or that
                      are all identical. Provided that the time evolution drives
                      the whole system from the initial state toward a scaling
                      state, a state which has similar properties as states
                      belonging to the class of quantum states for which we
                      derived the scaling relationship, the scaling prediction
                      holds. We examine various interaction parameters and initial
                      states for our model system to find whether or not the time
                      evolution reaches the class of states that have the scaling
                      property. For the homogeneous ring we find that the
                      evolution for select initial states does not reach these
                      scaling states. This conclusion is not modified if we add
                      some homogeneous random connections. For a ring we find that
                      some randomness in the interaction parameters is required so
                      that most initial configurations are driven toward the
                      scaling state. Furthermore, if the amount of randomness is
                      small the time required to reach the scaling states may be
                      very large. For the case of all random interactions in E the
                      ring is driven toward the scaling state. Adding small world
                      bonds between S and E with random interaction strengths may
                      decrease the time required to reach the scaling state or may
                      prevent the scaling state from being reached. For the latter
                      case we show that increasing the complexity of the
                      environment by adding extra connections within the
                      environment suffices to observe the predicted scaling
                      behavior.},
      cin          = {JSC},
      ddc          = {530},
      cid          = {I:(DE-Juel1)JSC-20090406},
      pnm          = {411 - Computational Science and Mathematical Methods
                      (POF2-411)},
      pid          = {G:(DE-HGF)POF2-411},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000315143200002},
      doi          = {10.1103/PhysRevA.87.022117},
      url          = {https://juser.fz-juelich.de/record/133045},
}