相关论文: Analytic bound on the excess charge for the Hartre…
In this note, we show that quantum lower bounds obtained using the adversary method hold in the Hamiltonian oracle model.
In this small paper, we study a boundary value problem for an equation of parabolic-hyperbolic type. The goal is to show how we can prove existence and uniqueness theorem for a regular solution.
The critical nuclear charge Zc required for a heliumlike atom to have at least one bound state was recently determined with high accuracy from variational calculations. Analysis of the wave functions further suggested that the bound state…
Force fields uniquely assign interatomic forces for a given set of atomic coordinates. The underlying assumption is that electrons are in their quantum-mechanical ground state or in thermal equilibrium. However, there is an abundance of…
We consider the fractional Hartree equation in the $L^2$-supercritical case, and we find a sharp threshold of the scattering versus blow-up dichotomy for radial data: If $ M[u_{0}]^{\frac{s-s_c}{s_c}}E[u_{0}<M[Q]^{\frac{s-s_c}{s_c}}E[Q]$…
We study bond percolation for a family of infinite hyperbolic graphs. We relate percolation to the appearance of homology in finite versions of these graphs. As a consequence, we derive an upper bound on the critical probabilities of the…
A scalar field gravitational analog of the Reissner-Nordstrom solution is investigated. The nonlinear Newtonian model has an upper-limit of charge for a central mass which agrees with the general relativistic condition required for the…
Recently, a precise measurement on the bound electron g factor in hydrogen-like carbon was performed [1]. We consider the present status of the theory of the g factor of an electron bound in a hydrogen-like atom and discuss new…
Absorbing boundary conditions in the form of a complex absorbing potential are routinely introduced in the Schr\"odinger equation to limit the computational domain or to study reactive scattering events using the multi-configurational…
We study systems containing electrons and nuclei. Based on the fact that the thermodynamic limit exists for systems with Dirichlet boundary conditions, we prove that the same limit is obtained if one imposes other boundary conditions such…
The aim of this paper is to introduce a new incremental procedure that can be used for numerical evaluation of the limit load. Existing incremental type methods are based on parametrization of the energy by the loading parameter…
It is shown that, in the self-consistent quantum statistical Hartree-Fock approximation, the number of electronic states localized on one nucleus is finite. This result is obtained on the basis of the general electron-nuclear model of…
The hydrogen atom as relativistic bound-state system of a proton and an electron in the complex-mass scheme is investigated. Interaction of a proton and an electron in the atom is described by the Lorentz-scalar Coulomb potential; the…
We study a non-linear Schroedinger equation with a Hartree-type nonlinearity and a localized random time-dependent external potential. Sharp dispersive estimates for the linear Schroedinger equation with a random time-dependent potential…
A new and simple analytical charge-control model of the two-dimensional electron gas of a double-heterojunction AlGaAs/GaAs/AlGaAs HEMT is described. It is found that, despite its simplicity, the charge-control model gives an accurate…
Under some conditions we give a blow-up analysis for solutions of an equation with Dirichlet boundary condition.
In this paper, we study additive properties of finite sets of lattice points on spheres in $3$ and $4$ dimensions. Thus, given $d,m \in \mathbb{N}$, let $A$ be a set of lattice points $(x_1, \dots, x_d) \in \mathbb{Z}^d$ satisfying $x_1^2 +…
A recently proposed strongly correlated electron system associated with the Temperley-Lieb algebra is solved by means of the coordinate Bethe ansatz for periodic and closed boundary conditions.
The simulation of ion-atom collisions remains a formidable challenge due to the complex interplay between electronic and nuclear degrees of freedom. We present a hybrid quantum-classical computing framework for simulating time-dependent…
The explicit semiclassical treatment of the logarithmic perturbation theory for the bound-state problem for the spherical anharmonic oscillator is developed. Based upon the $\hbar$-expansions and suitable quantization conditions a new…