Matrix-valued quantum lattice Boltzmann method

Christian B. Mendl ()
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Christian B. Mendl: Zentrum Mathematik, Technische Universität München, Boltzmannstraße 3, 85747 Garching bei München, Germany

International Journal of Modern Physics C (IJMPC), 2015, vol. 26, issue 10, 1-21

Abstract: 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.

Keywords: Quantum Boltzmann equation; lattice Boltzmann method (LBM); spin systems; quantum transport; spintronics (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1142/S0129183115501132

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