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@ARTICLE{Jin:13703,
      author       = {Jin, F. and De Raedt, H. and Yuan, S. and Katsnelson, M.I.
                      and Miyashita, S. and Michielsen, K.},
      title        = {{A}pproach to {E}quilibrium in {N}ano-scale {S}ystems at
                      {F}inite {T}emperature},
      journal      = {Journal of the Physical Society of Japan},
      volume       = {79},
      issn         = {0031-9015},
      address      = {Tokyo},
      publisher    = {The Physical Society of Japan},
      reportid     = {PreJuSER-13703},
      pages        = {124005},
      year         = {2010},
      note         = {This work is partially supported by NCF, the Netherlands,
                      by a Grant-in-Aid for Scientific Research on Priority Areas,
                      and the Next Generation Super Computer Project, Nano-science
                      Program from the Ministry of Education, Culture, Sports,
                      Science and Technology, Japan. Part of the calculations were
                      performed on the JUGENE supercomputer at JSC.},
      abstract     = {We study the time evolution of the reduced density matrix
                      of a system of spin-1/2 particles interacting with an
                      environment of spin-1/2 particles. The initial state of the
                      composite system is taken to be a product state of a pure
                      state of the system and a pure state of the environment. The
                      latter pure state is prepared such that it represents the
                      environment at a given finite temperature in the canonical
                      ensemble. The state of the composite system evolves
                      according to the time-dependent Schrodinger equation, the
                      interaction creating entanglement between the system and the
                      environment. It is shown that independent of the strength of
                      the interaction and the initial temperature of the
                      environment, all the eigenvalues of the reduced density
                      matrix converge to their stationary values, implying that
                      also the entropy of the system relaxes to a stationary
                      value. We demonstrate that the difference between the
                      canonical density matrix and the reduced density matrix in
                      the stationary state increases as the initial temperature of
                      the environment decreases. As our numerical simulations are
                      necessarily restricted to a modest number of spin-1/2
                      particles (<36), but do not rely on time-averaging of
                      observables nor on the assumption that the coupling between
                      system and environment is weak, they suggest that the
                      stationary state of the system directly follows from the
                      time evolution of a pure state of the composite system, even
                      if the size of the latter cannot be regarded as being close
                      to the thermodynamic limit.},
      keywords     = {J (WoSType)},
      cin          = {JSC},
      ddc          = {530},
      cid          = {I:(DE-Juel1)JSC-20090406},
      pnm          = {Scientific Computing (FUEK411) / 411 - Computational
                      Science and Mathematical Methods (POF2-411)},
      pid          = {G:(DE-Juel1)FUEK411 / G:(DE-HGF)POF2-411},
      shelfmark    = {Physics, Multidisciplinary},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000285532600021},
      doi          = {10.1143/JPSJ.79.124005},
      url          = {https://juser.fz-juelich.de/record/13703},
}