Related papers: Local Energy Optimality of Periodic Sets
The localized Hartree-Fock potential has proven to be a computationally efficient alternative to the optimized effective potential, preserving the numerical accuracy of the latter and respecting the exact properties of being…
A systematic first-principle study is performed to calculate the lattice parameters, electronic structure, and thermodynamic properties of UN using the local-density approximation (LDA)+\emph{U} and the generalized gradient approximation…
We present a new linear scaling method for the energy minimization step of semiempirical and first-principles Hartree-Fock and Kohn-Sham calculations. It is based on the self-consistent calculation of the optimum localized orbitals of any…
Let $M$ be a perfect matching on a set of points in the plane where every edge is a line segment between two points. We say that $M$ is globally maximum if it is a maximum-length matching on all points. We say that $M$ is $k$-local maximum…
We utilize recently introduced linear programming bounds for the energy of periodic configurations in $\mathbb{R}^d$ to construct configurations which are universally optimal among those of the form $\omega_4+L_\beta$, where $\omega_4$ is a…
The optimized effective potential method is formulated as a convex minimization problem. This formulation does not require assumptions about $v$-representability nor functional differentiability. The formulation provides a natural framework…
We employ correlation-consistent effective core potentials (ccECPs) to perform exact or nearly exact correlation and total energy calculations for the fifth-row elements (Rb-Xe). Total energies are calculated using various correlated…
We study the time regularity of local weak solutions of the heat equation in the context of local regular symmetric Dirichlet spaces. Under two basic and rather minimal assumptions, namely, the existence of certain cut-off functions and a…
By using the variational minimizing method with a special constraint and the direct variational minimizing method without constraint, we study second order Hamiltonian systems with a singular potential $V\in C^2(R^n\backslash O,R)$ and…
We investigate a stochastic heat engine based on an over-damped particle diffusing on the positive real axis in an externally driven time-periodic log-harmonic potential. The periodic driving is composed of two isothermal and two adiabatic…
Using the optimized effective potential method in conjunction with the semi-analytical approximation due to Krieger, Li and Iafrate, we have performed fully self-consistent exact exchange-only density-functional calculations for diatomic…
We investigate the role of energy, i.e. average photon number, as a resource in the computational complexity of bosonic systems. We show three sets of results: (1. Energy growth rates) There exist bosonic gate sets which increase energy…
Let $L_d$ be the Latt\`es map associated to the multiplication-by-$d$ endomorphism of an elliptic curve $E$ defined over a finite field $\mathbb{F}_q$. We determine the density $\delta(L_d,q)$ of periodic points for $L_d$ in…
Atomic basis sets are widely employed within quantum mechanics based simulations of matter. We introduce a machine learning model that adapts the basis set to the local chemical environment of each atom, prior to the start of self…
Despite recent advances, systematic quantitative treatment of the electron correlation problem in extended systems remains a formidable task. Systematically improvable Green's function methods capable of quantitatively describing weak and…
Using the recently developed theory of rigorously validated numerics, we address the Phase-Field-Crystal (PFC) model at the microscopic (atomistic) level. We show the existence of critical points and local minimizers associated with…
The Hausdorff dimension of a set can be detected using the Riesz energy. Here, we consider situations where a sequence of points, $\{x_n\}$, ``fills in'' a set $E \subset \mathbb{R}^d$ in an appropriate sense and investigate the degree to…
We consider several non-standard discrete and continuous Green energy problems in the complex plane and study the asymptotic relations between their solutions. In the discrete setting, we consider two problems; one with variable particle…
We prove that among all 1-periodic configurations $\Gamma$ of points on the real line $\mathbb{R}$ the quantities $$ \min_{x \in \mathbb{R}} \sum_{\gamma \in \Gamma} e^{- \pi \alpha (x - \gamma)^2} \quad \text{and} \quad \max_{x \in…
We present a detailed study of the use of localized spherical-wave basis sets, first introduced in the context of linear-scaling, in first-principles density-functional calculations. Several parameters that control the completeness of this…