Spectroscopic methods based on terahertz (THz) radiation can represent an innovative approach in the Cultural Heritage field. Specifically, contemporary and historical pigments can exhibit unique fingerprints. However, despite the high selectiveness of terahertz technique, the origin of spectral characteristics is not often known. In this work, the characteristic terahertz-time-domain spectroscopy spectrum of atacamite is reported in the spectral range 0.1–3.7 THz along with ab initio calculation of lattice dynamics to assess the nature of experimental features. The obtained results enable the acquisition of reliable new data in Heritage sciences, which is essential for developing accurate reference pigment databases.

We consider the perturbative renormalization of the Schwinger–Dyson functional, which is the generating functional of the expectation values of the products of the composite operator given by the field derivative of the action. It is argued that this functional plays an important role in the topological Chern–Simons and BF quantum field theories. It is shown that, by means of the renormalized perturbation theory, a canonical renormalization procedure for the Schwinger–Dyson functional is obtained. The combinatoric structure of the Feynman diagrams is illustrated in the case of scalar models. For the Chern–Simons and the BF gauge theories, the relationship between the renormalized Schwinger–Dyson functional and the generating functional of the correlation functions of the gauge fields is produced.

This work presents a systematic theoretical investigation and band-structure engineering of p-doped Ge/Si1−xGex multiple quantum wells (MQWs) tailored for mid-infrared (MIR) photonics. Using a self-consistent 6-band k·p Poisson-Schrödinger approach, we establish a predictive simulation framework that rigorously accounts for quantum confinement, epitaxial strain, and many-body interactions. A key feature of our model is the integration of realistic graded interfacial profiles and self-consistent many-body corrections—specifically local density approximation exchange—correlation and depolarization shifts. We demonstrate that these corrections are essential to resolve the observed 8–12 meV energy blueshift in high-density hole gases (> 1018cm−3), where standard single-particle approximations fail. By systematically optimizing well geometry, doping profiles, and Ge concentration, we achieve precise spectral tunability across the strategic 6–15 μm atmospheric window. Furthermore, our transport and optical models capture the complex valence band mixing between heavy, light, and split-off hole states, providing deep insights into intersubband absorption dynamics. The model's high predictive accuracy (> 95% compared to experimental MIR absorption spectra) establishes it as an indispensable tool for the ab-initio design of CMOS-compatible MIR emitters, quantum cascade lasers, and photodetectors. Ultimately, this framework bridges the gap between fundamental valence band physics and practical device performance, accelerating the development of next-generation monolithic silicon-photonics platforms. Received: 13 January 2026 | Revised: 14 April 2026 | Accepted: 22 June 2026 Conflicts of Interest The author declares that she has no conflicts of interest to this work. Data Availability Statement Data supporting the findings of this study are available from the corresponding author upon reasonable request. Author Contribution Statement Vittoria Urso: Conceptualization, Methodology, Software, Validation, Formal analysis, Investigation, Resources, Data curation, Writing – original draft, Writing – review & editing, Visualization, Supervision, Project administration.

We investigate the behavior of three-dimensional 3D exchange energy functional of density-functional theory in anisotropic systems with two-dimensional 2D character and 1D character. The local density approximation (LDA), the generalized gradient approximation (GGA), and the meta-GGA behave as functions of quantum well width. We use the infinite-barrier model (IBM) for the quantum well. In the first section, we describe the problem of three-dimensional exchange functional, in the second section we introduce the quasi-2D IBM system, in the third section we introduce the quasi-1D IBM system. Using that an exact-exchange functional provides the correct approach to the true two-dimensional limit, we want to show that the 2D limit can be considered as a constraint on approximate functionals. For the 1D limit case we also propose a new functional obtained with methods completely similar to those of 2D limit.