Systematic corrections to the Thomas-Fermi approximation without a gradient expansion

作者：Chau Thanh Tri^*; Hue Jun Hao^*; Trappe Martin I**jorn^*; Englert Berthold Georg^*

来源：New Journal of Physics, 2018, 20(7): 073003.

DOI：10.1088/1367-2630/aacde1

• orbital-free density-functional theory
• degenerate fermion systems
• semiclassical methods
• split-operator approximation
• gradient expansion
• high-order leapfrog

We improve on the Thomas-Fermi approximation for the single-particle density of fermions by introducing inhomogeneity corrections. Rather than invoking a gradient expansion, we relate the density to the unitary evolution operator for the given effective potential energy and approximate this operator by a Suzuki-Trotter factorization. This yields a hierarchy of approximations, one for each approximate factorization. For the purpose of a first benchmarking, we examine the approximate densities for a few cases with known exact densities and observe a very satisfactory, and encouraging, performance. As a bonus, we also obtain a simple fourth-order leapfrog algorithm for the symplectic integration of classical equations of motion.

• 出版日期2018-7-4