相关论文: Are natural orbitals useful for generating an effi…

For a non-relativistic particle, we consider the evolution of wave functions that consist of polynomial segments, usually joined smoothly together. These spline wave functions are compact (that is, they are initially zero outside a finite…

Using finite basis sets, it is shown how to construct a local Hamiltonian, such that one of its infinitely many degenerate eigenfunctions is the ground state full configuration interaction (FCI) wave function in that basis set. Formally,…

We study theoretically the low-energy hole states in Si, Ge, and Ge/Si core/shell nanowires (NWs). The NW core in our model has a rectangular cross section, the results for a square cross section are presented in detail. In the case of Ge…

The original formulation (Phys. Rev. Lett. 119, 063002, 2017) of the natural orbital functional - second-order M{\o}ller-Plesset (NOF-MP2) method is based on the MP2 that uses the canonical Hartree-Fock molecular orbitals. The current work…

The evolution of the centre-of-mass wave-function for a mesoscopic particle according to the Schr\"odinger-Newton equation can be approximated by a harmonic potential, if the wave-function is narrow compared to the size of the particle. It…

Using principles of asymptotic analysis, we derive the exact leading corrections to the Thomas-Fermi kinetic energy approximation for Kohn-Sham electrons for slabs. This asymptotic expansion approximation includes crucial quantum…

Approximating a function with a finite series, e.g., involving polynomials or trigonometric functions, is a critical tool in computing and data analysis. The construction of such approximations via now-standard approaches like least squares…

We derive a non-empirical, orbital-free density functional for the total energy of interacting electrons in two dimensions. The functional consists of a local formula for the interaction energy, where we follow the lines introduced by Parr…

Let ${\mathcal A}\subset {\mathcal P}(X)$, $\emptyset, X\in {\mathcal A}$, ${\mathcal A}$ being closed under finite intersections. If $\psi={o},\omega,\gamma$, then $\Psi({\mathcal A})$ is the family of those $\psi$-covers ${\mathcal U}$…

We consider gradient descent and quasi-Newton algorithms to optimize the full configuration interaction (FCI) ground state wavefunction starting from an arbitrary reference state $|0 \rangle$. We show that the energies obtained along the…

In this study, a new expansion of planetary disturbing function is developed for describing the resonant dynamics of minor bodies with arbitrary inclinations and semimajor axis ratios. In practice, the disturbing function is expanded around…

The quasi-streamfunction (Psi) formalism proposed by Kim et. al. (J.W. Kim, K.J. Bai, R.C. Ertekin, W.C. Webster, J. Eng. Math. 40, 17 (2001)) provides a natural framework for systematically studying zero-vorticity waves over arbitrary…

Numerical optimization is used to construct new orthonormal compactly supported wavelets with Sobolev regularity exponent as high as possible among those mother wavelets with a fixed support length and a fixed number of vanishing moments.…

Natural optical activity (NOA), the ability of a material to rotate the plane of polarized light, has traditionally been associated with structural chirality. However, this relationship has often been oversimplified, leading to conceptual…

In this work, we investigated the motion of spinning test particles around a rotating wormhole, extending, in this way, the previous work of Benavides-Gallego et al. in [Phys. Rev. D 101, no.12, 124024] to the general case. Using the…

$f$-electron systems exhibit a subtle interplay between strong spin--orbit coupling and crystal-field effects, producing complex energy landscapes that are computationally demanding. We introduce auxiliary functions, constructed by…

We calculate the two-particle irreducible (2PI) effective potential of the O(N) linear sigma model in 1+1 dimensions. The approximations we use are the next-to-leading order of a 1/N expansion (for arbitrary N) and a kind of "resummed loop…

From a secular Hamiltonian up to the quadrupole level with general relativity (GR), we study nodal circulations with orbital flips of test particles of the Habitable Zone (HZ) around a solar-mass star, which are perturbed by an inner…

Starting with just the assumption of uniformly distributed orbital orientations, we derive expressions for the distributions of the Keplerian orbital elements as functions of arbitrary distributions of eccentricity and semi-major axis. We…

I set out the 2PI formalism for quantum fields in a Friedmann-Robertson-Walker Universe. I show how one can solve self-consistently for the quantum field evolution and the evolution of the cosmological scale factor, using a renormalised…