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.     

Formation of Finely Dispersed Structures in Alloys of Aluminum with Cobalt and Zirconium

Russian Journal of Physical Chemistry A - Rapidly quenched alloys of aluminum with cobalt and zirconium are investigated using a combination of means of physicochemical analysis to study the...     

Gamma peak search and peak fitting algorithm for a low-resolution detector with applications in gamma spectroscopy

A Savitzky–Golay filtering for smoothing and peak search written in Python is presented in this paper alongside its applications in the list-mode digital data acquisition dual gamma–gamma coincidence bismuth germanate (BGO) detector. The study has demonstrated that the software provides a reliable and effective way to quantify trace amounts of ²²Na and ⁷Be in aerosol samples collected at Resolute Bay, Canada with a critical limit of 3 mBq and 5 Bq respectively for a 20 h counting interval, which are believed to be the inherent limitations of the dual-BGO system.

     

Preparation and gas sensing activity of La and Y co-doped titania nanoparticles

Journal of Sol-Gel Science and Technology - A novel gas sensing material, La–Y co-doped TiO2 nanoparticles, was synthesized by sol–gel method and applied to detect organic pollutants...     

A dynamic dissemination model for recurring online public opinion

Nonlinear Dynamics - With an increasing number of people sharing feelings and opinions online, the online platforms have become one of the most important channels for public opinion dissemination....