Structure of the first order Reduced Density Matrix in three electron systems: A Generalized Pauli Constraints assisted study

We investigate the structure of the one-body Reduced Density Matrix (1RDM) of three electron systems, i.e. doublet and quadruplet spin configurations, corresponding to the smallest interacting system with an open-shell ground state. To this end, we use Configuration Interaction (CI) expansions of the exact wave function in Slater determinants built from natural orbitals in a finite dimensional Hilbert space. With the exception of maximally polarized systems, the natural orbitals of spin eigenstates are generally spin dependent, i.e. the spatial parts of the up and down natural orbitals form two different sets. A measure to quantify this spin dependence is introduced and it is shown that it varies by several orders of magnitude depending on the system. We also study the ordering issue of the spin-dependent occupation numbers which has practical implications in Reduced Density Matrix Functional Theory minimization schemes when Generalized Pauli Constraints are imposed and in the form of the CI expansion in terms of the natural orbitals. Finally, we discuss the aforementioned CI expansion when there are GPCs that are almost "pinned"

Local reduced-density-matrix-functional theory: Incorporating static correlation effects in Kohn-Sham equations

We propose a novel scheme to bring reduced density matrix functional theory (RDMFT) into the realm of density functional theory (DFT) that preserves the accurate density functional description at equilibrium, while incorporating accurately static and left-right correlation effects in molecules and keeping the good computational performance of DFT-based schemes. The key ingredient is to relax the requirement that the local potential is the functional derivative of the energy with respect to the density. Instead, we propose to restrict the search for the approximate natural orbitals within a domain where these orbitals are eigenfunctions of a single-particle hamiltonian with a local effective potential. In this way, fractional natural occupation numbers are accommodated into Kohn-Sham equations allowing for the description of molecular dissociation without breaking spin symmetry. Additionally, our scheme provides a natural way to connect an energy eigenvalue spectrum to the approximate natural orbitals and this spectrum is found to represent accurately the ionization potentials of atoms and small molecules

Conditions for describing triplet states in reduced density matrix functional theory

We consider necessary conditions for the one-body-reduced density matrix (1RDM) to correspond to a triplet wave-function of a two electron system. The conditions concern the occupation numbers and are different for the high spin projections, $S_z=\pm 1$, and the $S_z=0$ projection. Hence, they can be used to test if an approximate 1RDM functional yields the same energies for both projections. We employ these conditions in reduced density matrix functional theory calculations for the triplet excitations of two-electron systems. In addition, we propose that these conditions can be used in the calculation of triplet states of systems with more than two electrons by restricting the active space. We assess this procedure in calculations for a few atomic and molecular systems. We show that the quality of the optimal 1RDMs improves by applying the conditions in all the cases we studied

Generalized Pauli constraints in reduced density matrix functional theory

Functionals of the one-body reduced density matrix (1-RDM) are routinely minimized under Coleman's ensemble $N$-representability conditions. Recently, the topic of pure-state $N$-representability conditions, also known as generalized Pauli constraints, received increased attention following the discovery of a systematic way to derive them for any number of electrons and any finite dimensionality of the Hilbert space. The target of this work is to assess the potential impact of the enforcement of the pure-state conditions on the results of reduced density-matrix functional theory calculations. In particular, we examine whether the standard minimization of typical 1-RDM functionals under the ensemble $N$-representability conditions violates the pure-state conditions for prototype 3-electron systems. We also enforce the pure-state conditions, in addition to the ensemble ones, for the same systems and functionals and compare the correlation energies and optimal occupation numbers with those obtained by the enforcement of the ensemble conditions alone

Friedel oscillations of one-dimensional correlated fermions from perturbation theory and density functional theory

We study the asymptotic decay of the Friedel density oscillations induced by an open boundary in a one-dimensional chain of lattice fermions with a short-range two-particle interaction. From Tomonaga-Luttinger liquid theory it is known that the decay follows a power law, with an interaction dependent exponent, which, for repulsive interactions, is larger than the noninteracting value $-1$. We first investigate if this behavior can be captured by many-body perturbation theory for either the Green function or the self-energy in lowest order in the two-particle interaction. The analytic results of the former show a logarithmic divergence indicative of the power law. One might hope that the resummation of higher order terms inherent to the Dyson equation then leads to a power law in the perturbation theory for the self-energy. However, the numerical results do not support this. Next we use density functional theory within the local-density approximation and an exchange-correlation functional derived from the exact Bethe ansatz solution of the translational invariant model. While the numerical results are consistent with power-law scaling if systems of $10^4$ or more lattice sites are considered, the extracted exponent is very close to the noninteracting value even for sizeable interactions.Comment: 11 pages, 5 figure

Equilibrium finite-frequency noise of an interacting mesoscopic capacitor studied in time-dependent density functional theory

We calculate the frequency-dependent equilibrium noise of a mesoscopic capacitor in time-dependent density functional theory (TDDFT). The capacitor is modeled as a single-level quantum dot with on-site Coulomb interaction and tunnel coupling to a nearby reservoir. The noise spectra are derived from linear-response conductances via the fluctuation-dissipation theorem. Thereby, we analyze the performance of a recently derived exchange-correlation potential with time-nonlocal density dependence in the finite-frequency linear-response regime. We compare our TDDFT noise spectra with real-time perturbation theory and find excellent agreement for noise frequencies below the reservoir temperature.Comment: to appear in Journal of Physics: Conference Series, 28th International Conference on Low Temperature Physics (LT28

Nonadiabatic Dynamics in Single-Electron Tunneling Devices with Time-Dependent Density-Functional Theory

We simulate the dynamics of a single-electron source, modeled as a quantum dot with on-site Coulomb interaction and tunnel coupling to an adjacent lead in time-dependent density-functional theory. Based on this system, we develop a time-nonlocal exchange-correlation potential by exploiting analogies with quantum-transport theory. The time nonlocality manifests itself in a dynamical potential step. We explicitly link the time evolution of the dynamical step to physical relaxation timescales of the electron dynamics. Finally, we discuss prospects for simulations of larger mesoscopic systems

Iatrogene Netzhautdefekte nach intravitrealer operativer Medikamenteneingabe

Hintergrund Intravitreale operative Medikamenteneingaben (IVOM) stellen einen der häufigsten Eingriffe in der Medizin dar. Das Risikoprofil ist gering. Neben intraokularen Drucksteigerungen zählen insbesondere erregerbedingte Endophthalmitiden, Glaskörperblutungen und rhegmatogene Netzhautablösungen zu den gängigen Komplikationen. Darüber hinaus wurden auch einzelne Fälle von Linsenverletzungen sowie peripheren Netzhautdefekten und Makulaforamina in Assoziation mit vitreoretinalen Traktionen beschrieben. In der hier vorliegenden Fallserie berichten wir über scharfe iatrogene Netzhaut- bzw. Makulaverletzungen. Methoden Multizentrische Fallsammlung von IVOM-Patienten mit iatrogenen Netzhautdefekten, retrospektiv über den Zeitraum 2016 bis 2023. Ergebnisse Es konnten 9 Fälle (72 Jahre ± 8,1, 3 Augen pseudophak) mit einem iatrogenen retinalen Trauma nach IVOM zur Therapie einer neovaskulären altersbedingten Makuladegeneration (nAMD) dokumentiert werden. Während in 6 Fällen scharfe Verletzungen innerhalb der Makula vorlagen, waren die Läsionen in den anderen Fällen extramakulär lokalisiert. Schlussfolgerungen Iatrogene Netzhaut- und Makulaverletzungen sind seltene Komplikationen im Rahmen der IVOM und bei sachgemäßer Durchführung insbesondere mit Blick auf die Kanülenverwendung und die Wahl des Limbusabstands vermeidbar