The coupled-cluster formalism – a mathematical perspective

ABSTRACT

The Coupled-Cluster (CC) theory is one of the most successful high precision methods used to solve the stationary Schrödinger equation. In this article, we address the mathematical foundation of this theory with focus on the advances made in the past decade. Rather than solely relying on spectral gap assumptions (non-degeneracy of the ground state), we highlight the importance of coercivity assumptions – Gårding type inequalities – for the local uniqueness of the CC solution. Based on local strong monotonicity, different sufficient conditions for a local unique solution are suggested. One of the criteria assumes the relative smallness of the total cluster amplitudes (after possibly removing the single amplitudes) compared to the Gårding constants. In the extended CC theory the Lagrange multipliers are wave function parameters and, by means of the bivariational principle, we here derive a connection between the exact cluster amplitudes and the Lagrange multipliers. This relation might prove useful when determining the quality of a CC solution. Furthermore, the use of an Aubin–Nitsche duality type method in different CC approaches is discussed and contrasted with the bivariational principle.     

单晶硅晶格间距的测量技术进展及应用

单晶硅晶格间距是许多重要物理常数测量的基础。本文介绍了硅晶格间距测量技术的发展历程,包括X射线干涉仪直接测量和晶格比较仪间接测量两种方法,以及影响测量结果不确定度的关键因素。得益于晶格间距测量的进展,在纳米尺度,硅晶格间距被国际计量局(BIPM)批准成为新的米定义复现形式。最后介绍了硅晶格在计量学中的应用,以及基于硅晶格实现纳米几何量测量的溯源体系的研究趋势。     

Efficient Quantum Dot Light-Emitting Diodes Based on Well-Type Thick-Shell CdxZn1−xS/CdSe/CdyZn1−yS Quantum Dots

Device grade quantum dots (QDs) require QDs ensembles to retain their original superior optical properties as in solution. QDs with thick shells are proven effective in suppressing the inter-dot interaction and preserving the emission properties for QDs solids. However, lattice strain–induced defects may form as the shell grows thicker, resulting in a notable photoluminescence quenching. Herein, a well-type Cd_xZn_1−xS/CdSe/Cd_yZn_1−yS QDs is proposed, where ternary alloys CdZnS are adopted to match the lattice parameter of intermediate CdSe by separately adjusting the x and y parameters. The resultant thick-shell Cd_0.5Zn_0.5S/CdSe/Cd_0.73Zn_0.27S QDs reveal nonblinking properties with a high PL QY of 99% in solution and 87% in film. The optimized quantum dot light-emitting diodes (QLEDs) exhibit a luminance of 31547.5 cd m⁻² at the external quantum efficiency maximum of 21.2% under a bias of 4.0 V. The shell thickness shows great impact on the degradation of the devices. The T₅₀ lifetime of the QLEDs with 11.2 nm QDs reaches 251 493 h, which is much higher than that of 6.5 and 8.4 nm QDs counterparts. The performances of the well-type thick-shell QLEDs are comparable to state-of-the-art devices, suggesting that this type of QDs is a promising candidate for efficient optoelectronic devices.     

Spontaneous magnetization of the Ising model on a 4–8 lattice

The spontaneous magnetization of the Ising model on a 4–8 lattice with six different coupling constants and two different magnetic moments is studied. A formula for the spontaneous magnetization is proposed. The result agrees with the exact low-temperature series expansions up to the 12th order.     

An Analogue of Distributivity for Ungraded Lattices

In this paper, we study lattices that posess both the properties of being extremal (in the sense of Markowsky) and of being left modular (in the sense of Blass and Sagan). We call such lattices trim and show that they posess some additional appealing properties, analogous to those of a distributive lattice. For example, trimness is preserved under taking intervals and suitable sublattices. Trim lattices satisfy a weakened form of modularity. The order complex of a trim lattice is contractible or homotopic to a sphere; the latter holds exactly if the maximum element of the lattice is a join of atoms. Any distributive lattice is trim, but trim lattices need not be graded. The main example of ungraded trim lattices are the Tamari lattices and generalizations of them. We show that the Cambrian lattices in types A and B defined by Reading are trim; we conjecture that all Cambrian lattices are trim.     

推广x重新标度模型的重标度参数经验公式

给出了推广x重新标度模型的重标度参数经验公式,其中建立了重标度参数与原子核的平均结合能之间的联系,由该公式可以得出A≥12的所有核的重标度参数值,利用这些参数值可以计算有关核过程并做出预言.