Systematic corrections to the Thomas-Fermi approximation without a gradient expansion
Abstract
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.
- Publication:
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New Journal of Physics
- Pub Date:
- July 2018
- DOI:
- 10.1088/1367-2630/aacde1
- arXiv:
- arXiv:1709.01719
- Bibcode:
- 2018NJPh...20g3003C
- Keywords:
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- Condensed Matter - Quantum Gases;
- Physics - Atomic Physics;
- Quantum Physics
- E-Print:
- 20 pages