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Open Quantum Systems Decoherence

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

arXiv
Authors: Thanh Tri Chau, Jun Hao Hue, Martin-Isbjörn Trappe, Berthold-Georg Englert

Year

2017

Paper ID

7652

Status

Preprint

Abstract Read

~2 min

Abstract Words

104

Citations

N/A

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.

Why This Paper Matters

  • This paper contributes to the Open Quantum Systems & Decoherence research area in the Quantum Articles archive.
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  • We improve on the Thomas-Fermi approximation for the single-particle density of fermions by introducing inhomogeneity corrections.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1709.01719 [2] arXiv https://arxiv.org/abs/1709.01719 [3] Publisher https://arxiv.org/abs/1709.01719

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