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Abstract: |
We derived a series of high-order quantum moment models of the Wigner equation in (Cai, Fan, Li, Lu and Wang, J. Math. Phys., 2012). In this talk, I will discuss about how to extended this work to density function theory (DFT). The most popular implement of DFT is the Kohn-Sham equation, which transforms a many-particle interacting system into a fictitious non-interacting one-particle system. The Kohn-Sham equation is a non-linear Schr\"odinger equation, and the corresponding Wigner equation can be derived as an alternative implementation of DFT. We derived quantum hydrodynamic models of the Wigner equation by moment closure following in (Cai, Fan, Li, Lu and Wang, J. Math. Phys., 2012). The derived quantum hydrodynamic models are globally hyperbolic thus locally wellposed. The contribution of the Kohn-Sham potential is turned into a nonlinear source term of the hyperbolic moment system. This work provides a new possible way to solve DFT problems.
参考文献： Z.-N. Cai, Y.-W. Fan, R. Li, T. Lu and W.-Q. Yao, Quantum Hydrodynamic Model of Density Functional Theory, Journal of Mathematical Chemistry, DOI: 10.1007/s10910-013-0176-1. http://www.springerlink.com/openurl.asp?genre=article&id=doi:10.1007/s10910-013-0176-1 |
