Communications in Mathematical Sciences
Volume 10 (2012)
A fast spectral algorithm for the quantum Boltzmann collision operator
Pages: 989 – 999
This paper introduces a fast spectral algorithm for the quantum Boltzmann collision operator. In the usual spectral framework, one of the terms in the operator cannot be evaluated efficiently. The new approach is based on the fundamental property of the exponential function which allows one to construct a new decomposition of the collision kernel to speed up the computation. Numerical results in 2-D and 3-D for both the Bose gas and the Fermi gas are presented to illustrate the accuracy and efficiency of the method.
quantum Boltzmann equation, fast spectral method
2010 Mathematics Subject Classification