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

Jianfeng Lu, Christian B. Mendl

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

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.

Original languageEnglish
Pages (from-to)303-316
Number of pages14
JournalJournal of Computational Physics
Volume291
DOIs
StatePublished - 5 Jun 2015

Keywords

  • Fourier spectral method
  • Hubbard model
  • Quantum Boltzmann equation

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