Related papers: Energy approximation for some double phase functio…
We calculate the ground state energies of a system of two dipolar fermions trapped in a harmonic oscillator potential. The dipoles are assumed to be aligned parallel to each other. We perform the calculations of ground state energy as a…
We show, in several important and general cases, that a low variational energy density of a trial state is possible even when the trial state represents a different phase from the ground state. Specifically, we ask whether the ground state…
We introduce a general scheme to consistently truncate equations of motion for Green's functions. Our scheme is guaranteed to generate physical Green's functions with real excitation energies and positive spectral weights. There are free…
We consider a free-boundary and free-discontinuity energy connecting phase separation and fracture in an elastic material. The energy excludes the contribution of phase boundaries in the cracked region, providing a heuristic approximation…
We study the stability of a two-dimensional Lax-Wendroff scheme in a quarter-plane. Following our previous work, we aim here at adapting the energy method in order to study second order extrapolation boundary conditions. We first show on…
We propose a density functional to find the ground state energy and density of interacting particles, where both the density and the pair density can adjust in the presence of an inhomogeneous potential. As a proof of principle we formulate…
We analytically derive the lower bound of the total conformational energy of a protein structure by assuming that the total conformational energy is well approximated by the sum of sequence-dependent pairwise contact energies. The condition…
Using the Thomas-Fermi approximation, we show that an interacting two dimensional electron gas may be described in terms of fractional exclusion statistics at zero and finite temperatures when the interaction has a short-range component. We…
Two electrons at the threshold of ionization represent a severe test case for electronic structure theory. A pseudospectral method yields a very accurate density of the two-electron ion with nuclear charge close to the critical value.…
We introduce an approach to computing the free energy of quasicrystals, which we use to calculate phase diagrams for systems of two-dimensional patchy particles with five regularly arranged patches that have previously been shown to form…
Energies of quantum states are given by the arguments of phase-evolution exponentials. It follows then that an analysis of the energies of a two-state system (TSS) can revolve around phase-emphasized description of states' probability…
We develop a phase-field approximation of the relaxation of the perimeter functional in the plane under a connectedness constraint based on the classical Modica-Mortola functional and the connectedness constraint of (Dondl, Lemenant,…
Matrix elements of potential energy are examined in detail. We consider a model problem - a particle in a central potential. The most popular forms of central potential are taken up, namely, square-well potential, Gaussian, Yukawa and…
Interatomic potentials approximate the potential energy of atoms as a function of their coordinates. Their main application is the effective simulation of many-atom systems. Here, we review empirical interatomic potentials designed to…
We investigate analytically the performance of many-body energy functionals, derived respectively by Klein and Luttinger and Ward, at different levels of diagrammatic approximations, ranging from second Born, to GW, to the so-called…
Quantum vacuum energy (Casimir energy) is reviewed for a mathematical audience as a topic in spectral theory. Then some one-dimensional systems are solved exactly, in terms of closed classical paths and periodic orbits. The relations among…
An infinite sequence of potential well functions is considered. A trial wavefunction is used with the Schr$\ddot{\text{o}}$dinger equation to obtain an approximate ground state energy for each potential well function. We obtain an…
We establish necessary and sufficient conditions for the N-representability of the universal one-electron reduced density matrix functional. Functionals satisfying these conditions are guaranteed to yield variational upper bounds on the…
In the variational cluster approximation (VCA) (or variational cluster perturbation theory), widely used to study the Hubbard model, a fundamental problem that renders variational solutions difficult in practice is its known lack of…
Quality of approximations is an important issue in modelling nuclear matter. It is shown that the Pad{\' e} approximation provides a useful tool for describing the symmetry energy in highly asymmetric systems. The focus is on the symmetry…