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

JOURNAL OF COMPUTATIONAL PHYSICS

卷:291

Article

Lu, Jianfeng^1,2  Mendl, Christian B.³ 

[1] Duke Univ, Dept Math, Dept Phys, Durham, NC 27708 USA

[2] Duke Univ, Dept Chem, Durham, NC 27708 USA

[3] Tech Univ Munich, Dept Math, D-85747 Garching, Germany

关键词: Quantum Boltzmann equation;    Hubbard model;    Fourier spectral method;   

DOI  :  10.1016/j.jcp.2015.03.020

来源: Elsevier

【 摘 要 】

We develop an efficient algorithm for a spatially inhomogeneous matrix-valued quantum Boltzmann equation derived from the Hubbard model. The distribution functions are 2 x 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. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free