Numerical scheme for a spatially inhomogeneous matrix-valued quantum Boltzmann equation

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2015-06-05

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Abstract

© 2015 Elsevier Inc.We develop an efficient algorithm for a spatially inhomogeneous matrix-valued quantum Boltzmann equation derived from the Hubbard model. The distribution functions are 2 × 2 matrix-valued to accommodate the spin degree of freedom, and the scalar quantum Boltzmann equation is recovered as a special case when all matrices are proportional to the identity. We use Fourier discretization and fast Fourier transform to efficiently evaluate the collision kernel with spectral accuracy, and numerically investigate periodic, Dirichlet and Maxwell boundary conditions. Model simulations quantify the convergence to local and global thermal equilibrium.

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Published Version (Please cite this version)

10.1016/j.jcp.2015.03.020

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Lu, J, and CB Mendl (2015). Numerical scheme for a spatially inhomogeneous matrix-valued quantum Boltzmann equation. Journal of Computational Physics, 291. pp. 303–316. 10.1016/j.jcp.2015.03.020 Retrieved from https://hdl.handle.net/10161/14107.

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