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.     

Single-emissive-layer all-perovskite white light-emitting diodes employing segregated mixed halide perovskite crystals

Metal halide perovskites have demonstrated impressive properties for achieving efficient monochromatic light-emitting diodes. However, the development of white perovskite light-emitting diodes (PeLEDs) remains a big challenge. Here, we demonstrate a single-emissive-layer all-perovskite white PeLED using a mixed halide perovskite film as the emissive layer. The perovskite film consists of separated mixed halide perovskite phases with blue and red emissions, which are beneficial for suppressing halide anion exchange and preventing charge transfer. As a result, the white PeLED shows balanced white light emission with Commission Internationale de L''Eclairage coordinates of (0.33, 0.33). In addition, we find that the achievement of white light emission from mixed halide perovskites strongly depends on effective modulation of the halide salt precursors, especially lead bromide and benzamidine hydrochloride in our case. Our work provides very useful guidelines for realizing single-emissive-layer all-perovskite white PeLEDs based on mixed halide perovskites, which will spur the development of high-performance white PeLEDs.

We demonstrated a single-emissive-layer all-perovskite white light-emitting diode based on a mixed halide perovskite film.     

Electron Energy-Loss Spectroscopy Study of the Change in the Free-Electron Density in Thin Superconducting NbN Films under Ion-Beam Irradiation

The change in the free-electron density in ultrathin (5 nm) superconducting NbN films in the initial state and after irradiation by O⁺ ions to doses of (0.1–0.9) × 10¹⁷ cm^–2 has been studied by electron energy-loss spectroscopy (EELS). The analysis has been performed on cross section samples prepared by the focused ion beam method, using plasmon oscillations with energies up to 50 eV. The radiation-induced replacement of nitrogen atoms with oxygen atoms in niobium nitride is found to change the electrical properties of the material, which leads to a decrease in the free-electron density with an increase in the irradiation dose.     

Fluid‐structure coupling of linear elastic model with compressible flow models

Cavitation erosion is caused in solids exposed to strong pressure waves developing in an adjacent fluid field. The knowledge of the transient distribution of stresses in the solid is important to understand the cause of damaging by comparisons with breaking points of the material. The modeling of this problem requires the coupling of the models for the fluid and the solid. For this purpose, we use a strategy based on the solution of coupled Riemann problems that has been originally developed for the coupling of 2 fluids. This concept is exemplified for the coupling of a linear elastic structure with an ideal gas. The coupling procedure relies on the solution of a nonlinear equation. Existence and uniqueness of the solution is proven. The coupling conditions are validated by means of quasi‐1D problems for which an explicit solution can be determined. For a more realistic scenario, a 2D application is considered where in a compressible single fluid, a hot gas bubble at low pressure collapses in a cold gas at high pressure near an adjacent structure.