论文标题
玻色子的密度矩阵功能理论降低
Reduced Density Matrix Functional Theory for Bosons
论文作者
论文摘要
基于Hohenberg-Kohn定理的概括，我们提出了玻感量子系统的基态理论。由于它涉及一粒子降低的密度矩阵$γ$作为天然变量，但仍以精确的方式恢复量子相关性，因此特别适合对Bose-Einstein冷凝物的准确描述。作为原则的证明，我们研究了光学晶格的基础。发现了基础$ V $证明性问题的解决方案，其特殊形式将受限的搜索形式识别为构建准确功能近似值的理想起点：该$ n $ n $ boson Hubbard dimer和Bogoliubov一般的bogoliubov appproxapproximated系统的确切功能确定。发现各自的梯度力在Bose-Einstein凝结方面存在分歧，$ \nabla_γ\ Mathcal {f} \ propto 1/\ sqrt {1-n _ {\ Mathrm {bec}}}}}/n} $，为完整的自然缺乏提供了自然的解释。
Based on a generalization of Hohenberg-Kohn's theorem, we propose a ground state theory for bosonic quantum systems. Since it involves the one-particle reduced density matrix $γ$ as a natural variable but still recovers quantum correlations in an exact way it is particularly well-suited for the accurate description of Bose-Einstein condensates. As a proof of principle we study the building block of optical lattices. The solution of the underlying $v$-representability problem is found and its peculiar form identifies the constrained search formalism as the ideal starting point for constructing accurate functional approximations: The exact functionals for this $N$-boson Hubbard dimer and general Bogoliubov-approximated systems are determined. The respective gradient forces are found to diverge in the regime of Bose-Einstein condensation, $\nabla_γ \mathcal{F} \propto 1/\sqrt{1-N_{\mathrm{BEC}}/N}$, providing a natural explanation for the absence of complete BEC in nature.
