Numerical scheme for a spatially inhomogeneous matrix-valued quantum Boltzmann equation
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© 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.
Published Version (Please cite this version)10.1016/j.jcp.2015.03.020
Publication InfoLu, Jianfeng; & Mendl, CB (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 http://hdl.handle.net/10161/14107.
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Associate Professor of Mathematics
Jianfeng Lu is an applied mathematician interested in mathematical analysis and algorithm development for problems from computational physics, theoretical chemistry, materials science and other related fields.More specifically, his current research focuses include:Electronic structure and many body problems; quantum molecular dynamics; multiscale modeling and analysis; rare events and sampling techniques.