Matrix-valued quantum lattice Boltzmann method

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We devise a lattice Boltzmann method (LBM) for a matrix-valued quantum Boltzmann equation, with the classical Maxwell distribution replaced by Fermi-Dirac functions. To accommodate the spin density matrix, the distribution functions become 2 × 2 matrix-valued. From an analytic perspective, the efficient, commonly used BGK approximation of the collision operator is valid in the present setting. The numerical scheme could leverage the principles of LBM for simulating complex spin systems, with applications to spintronics.

Original languageEnglish
Article number1550113
JournalInternational Journal of Modern Physics C
Issue number10
StatePublished - 26 Oct 2015


  • Lattice Boltzmann method (LBM)
  • Quantum Boltzmann equation
  • Quantum transport
  • Spin systems
  • spintronics


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