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arXiv2026

Moreau-Yosida-based Kohn-Sham Inversion for Periodic Systems

Density-potential inversion for periodic systems within Moreau-Yosida-regularised density-functional theory is investigated, both theoretically and numerically. We develop the framework in a periodic homogeneous Sobolev space and use it to recover the exchange-correlation potential of Kohn-Sham theory through a limiting procedure. A key analytical ingredient is the proof of lower semicontinuity of the non-interacting kinetic-energy functional in the chosen topology. The proximal mapping, together with its algorithmic evaluation, plays a central role in the resulting inversion scheme. Numerical experiments illustrate the performance and properties of the method for both the Kohn-Sham and Gross-Pitaevskii equations.

math.NA↗

arXiv2025

Quantum-Electrodynamical Density-Functional Theory Exemplified by the Quantum Rabi Model

The key features of density-functional theory (DFT) within a minimalistic implementation of quantum electrodynamics are demonstrated, thus allowing to study elementary properties of quantum-electrodynamical density-functional theory (QEDFT). We primarily employ the quantum Rabi model, that describes a two-level system coupled to a single photon mode, and also discuss the Dicke model, where multiple two-level systems couple to the same photon mode. In these settings, the density variables of the system are the polarization and the displacement of the photon field. We give analytical expressions for the constrained-search functional and the exchange-correlation potential and compare to established results from QEDFT. We further derive a form for the adiabatic connection that is almost explicit in the density variables, up to only a non-explicit correlation term that gets bounded both analytically and numerically. This allows several key features of DFT to be studied without approximations.

quant-ph↗