Related papers: Energy functional for the three-level Lipkin model
Based on recent progress on fermionic exchange symmetry we propose a way to develop new functionals for reduced density matrix functional theory. For some settings with an odd number of electrons, by assuming saturation of the inequalities…
Starting with an orthogonal polynomial sequence $\{p_n(s)\}_{n=0}^\infty$ that has a discrete spectrum, we design an energy spectrum formula, $E_k = f (s_k)$, where $|{s_k\}$ is the finite or infinite discrete spectrum of the polynomial.…
We derive Hamiltonian flow equations giving the evolution of the Lipkin Hamiltonian to a diagonal form using continuous unitary transformations. To close the system of flow equations, we present two different schemes. First we linearize an…
A new kind of the relativistic three-body equations for the three fermion systems are suggested. These equations are derived in the framework of the standard field-theoretical $S$-matrix approach in the time-ordered three dimensional form.…
Energy-Based Models (EBMs) have proven to be a highly effective approach for modelling densities on finite-dimensional spaces. Their ability to incorporate domain-specific choices and constraints into the structure of the model through…
A potential energy curve (PEC) accurate to a fraction of 1 ppm ($1:10^6$) is computed for the $^3\Sigma_\mathrm{u}^+$ state of He$_2$ endowed with relativistic and QED corrections. The nuclear Schr\"odinger equation is solved on this PEC…
In recent work, generalized gradient approximations (GGA's) have been constructed from the energy density of the Airy gas for exchange but not for correlation. We report the random phase approximation (RPA) conventional correlation energy…
We propose a practicable method for describing linear dynamics of different finite Fermi systems. The method is based on a general self-consistent procedure for factorization of the two-body residual interaction. It is relevant for diverse…
This paper presents a new method for studying electromechanical transients in power systems using three phase, combined transmission and distribution models (hybrid models). The methodology models individual phases of an electric network…
The recent development of the accurate and efficient semilocal density functionals on the third rung of Jacob's ladder of density functional theory such as the revised regularized strongly constrained and appropriately normed (r2SCAN)…
The random-phase approximation to the ground state correlation energy (RPA) in combination with exact exchange (EX) has brought Kohn-Sham (KS) density functional theory one step closer towards a universal, "general purpose first principles…
We consider the effective potential in three-dimensional models with O(N) symmetry. For generic values of N, and in particular for the physically interesting cases N=0,1,2,3, we determine the six-point and eight-point renormalized coupling…
We address the few-body problem using the adiabatic hyperspherical representation. A general form for the hyperangular Green's function in $d$-dimensions is derived. The resulting Lippmann-Schwinger equation is solved for the case of…
We obtain the effective potential at finite temperature within the left-right symmetric model. We take the Higgs sector to consist of two doublets and calculate its finite temperature effective potential up to the order of…
We calculate two-point energy level correlation function in weakly disorderd metallic grain with taking account of localization corrections to the universal random matrix result. Using supersymmetric nonlinear sigma model and exactly…
We solve the random energy model when the energies of the configurations take only integer values. In the thermodynamic limit, the average overlaps remain size dependent and oscillate as the system size increases. While the extensive part…
The action of the long-range residual force on the expectation value of observables in the nuclear ground states is evaluated by finding optimal values for the coefficients of the canonical transformation which connects the phonon vacuum…
We investigate a highly-nonlocal generalization of the Lindhard function, given by the jellium-with-gap model. We find a band-gap-dependent gradient expansion of the kinetic energy, which performs noticeably well for large atoms. Using the…
Relativistic energy density functionals (REDF) provide a complete and accurate, global description of nuclear structure phenomena. A modern semi-empirical functional, adjusted to the nuclear matter equation of state and to empirical masses…
We explore several random phase approximation (RPA) correlation energy variants within the adiabatic-connection fluctuation-dissipation theorem approach. These variants differ in the way the exchange interactions are treated. One of these…