论文标题
确切的骨气激发的一颗粒子理论：从广义的Hohenberg-Kohn定理到共有N-占有性
An exact one-particle theory of bosonic excitations: From a generalized Hohenberg-Kohn theorem to convexified N-representability
论文作者
论文摘要
由Bose-Einstein凝结的Penrose-Onsager标准的激励，我们提出了一种功能理论，用于通过一颗粒子图片靶向玻色量量子系统的低洼激发能。为此，我们采用了雷利 - 里兹变异原理的扩展，以频谱$ \ boldsymbol {w} $进行整体状态，并证明了hohenberg-kohn定理的相应概括：基本的一方面一方面的一方面密度降低的密度矩阵确定了$ n $ n $ nestim $ n $ nestim $ n $ nestim $ n $ bolds n $ bolds in y $ bolds in n $ bolds in n $ bolds n $ bolds n $ \ bolds。然后，为了绕过功能理论常见的$ v $证明性问题，并处理能量的变性性，我们求助于Levy-lieb限制的搜索形式主义，并结合精确的凸出放松。相应的玻色子一体$ \ boldsymbol {w} $ - 集合$ n $ - 证实性问题得到了全面解决。值得注意的是，这揭示了在概念上类似于Pauli的Fermions的排除原则，并最近发现了其概括，这表明了骨骼排除原则的完整层次结构。
Motivated by the Penrose-Onsager criterion for Bose-Einstein condensation we propose a functional theory for targeting low-lying excitation energies of bosonic quantum systems through the one-particle picture. For this, we employ an extension of the Rayleigh-Ritz variational principle to ensemble states with spectrum $\boldsymbol{w}$ and prove a corresponding generalization of the Hohenberg-Kohn theorem: The underlying one-particle reduced density matrix determines all properties of systems of $N$ identical particles in their $\boldsymbol{w}$-ensemble states. Then, to circumvent the $v$-representability problem common to functional theories, and to deal with energetic degeneracies, we resort to the Levy-Lieb constrained search formalism in combination with an exact convex relaxation. The corresponding bosonic one-body $\boldsymbol{w}$-ensemble $N$-representability problem is solved comprehensively. Remarkably, this reveals a complete hierarchy of bosonic exclusion principle constraints in conceptual analogy to Pauli's exclusion principle for fermions and recently discovered generalizations thereof.
