保持非相互作用费米气体单体密度矩阵的隐性

IF 2 3区 物理与天体物理 Q2 PHYSICS, MATHEMATICAL
L M Farrell, D Eaton, P Chitnelawong, K Bencheikh, B P van Zyl
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引用次数: 0

摘要

零温非相互作用费米气体的单体密度矩阵(ODM)可以通过不同的ℏ展开技术在半经典体系中近似得到。我们期望每种近似 ODM 的方法都能得到等效密度矩阵,这些矩阵在ℏ 的任何阶都是赫米特和幂等的。然而,基尔日尼茨法和维格纳-柯克伍德法并不具备这些特性,而格拉马蒂奥斯-沃罗斯法却具备这些特性。在这里,我们通过对对称坐标的适当改变,明确地证明了对于任意的 d 维,每种方法确实是相同的、赫米特的和幂等的。这种变量变化解决了各种方法之间的不一致性,表明基尔日尼茨法和维格纳-柯克伍德法的非赫米提性和非等幂性行为是对半经典ℏ展开进行非对称截断的产物。我们的工作还首次明确推导了 d 维 Grammaticos-Voros ODM,它最初是由 Redjati 等人(2019 J. Phys. Chem. Solids 134 313-8)根据其 d=1,2,3,4 表达式提出的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Preserving the Hermiticity of the one-body density matrix for a non-interacting Fermi gas
The one-body density matrix (ODM) for a zero temperature non-interacting Fermi gas can be approximately obtained in the semiclassical regime through different -expansion techniques. One would expect that each method of approximating the ODM should yield equivalent density matrices which are both Hermitian and idempotent to any order in . However, the Kirzhnits and Wigner–Kirkwood methods do not yield these properties, while the Grammaticos–Voros method does. Here we show explicitly, for arbitrary d-dimensions through an appropriate change into symmetric coordinates, that each method is indeed identical, Hermitian, and idempotent. This change of variables resolves the inconsistencies between the various methods, showing that the non-Hermitian and non-idempotent behavior of the Kirzhnits and Wigner–Kirkwood methods is an artifact of performing a non-symmetric truncation to the semiclassical -expansions. Our work also provides the first explicit derivation of the d-dimensional Grammaticos–Voros ODM, originally proposed by Redjati et al (2019 J. Phys. Chem. Solids 134 313–8) based on their d=1,2,3,4 expressions.
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来源期刊
CiteScore
4.10
自引率
14.30%
发文量
542
审稿时长
1.9 months
期刊介绍: Publishing 50 issues a year, Journal of Physics A: Mathematical and Theoretical is a major journal of theoretical physics reporting research on the mathematical structures that describe fundamental processes of the physical world and on the analytical, computational and numerical methods for exploring these structures.
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