Related papers: Linear scaling solution of the all-electron Coulom…
In this paper we first derive a Coulomb Hamiltonian for electron--electron interaction in quantum dots in the Heisenberg picture. Then we use this Hamiltonian to enhance a Bloch model, which happens to be nonlinear in the density matrix.…
Accurate calculation of electrostatic potential and gradient on the molecular surface is highly desirable for the continuum and hybrid modeling of large scale deformation of biomolecules in solvent. In this article a new numerical method is…
We study equilibrium statistical mechanics of classical point counter-ions, formulated on 2D Euclidean space with logarithmic Coulomb interactions (infinite number of particles) or on the cylinder surface (finite particle numbers), in the…
Exact self-consistent particle-like solutions with spherical and/or cylindrical symmetry to the equations governing the interacting system of scalar, electromagnetic and gravitational fields have been obtained. As a particular case it is…
The original Thomson problem of "spherical crystallography" seeks the ground state of electron shells interacting via the Coulomb potential; however one can also study crystalline ground states of particles interacting with other…
We present a density-matrix rate-equation approach to sequential tunneling through a metal particle weakly coupled to ferromagnetic leads. The density-matrix description is able to deal with correlations between degenerate many-electron…
Reciprocal space methods for solving Poisson's equation for finite charge distributions are investigated. Improvements to previous proposals are presented, and their performance is compared in the context of a real-space density functional…
We consider the thermodynamics of a uniformly charged polyelectrolyte with harmonic bonds. For such a system there is at high temperatures an approximate scaling of global properties like the end-to-end distance and the interaction energy…
New non-linear, spatially periodic, long wavelength electrostatic modes of an electron fluid oscillating against a motionless ion fluid (Langmuir waves) are given, with viscous and resistive effects included. The cold plasma approximation…
This paper proposes a finite element method for solving the periodic steady-state problem for the scalar-valued and vector-valued Poisson equations, a simple reduction model of the Maxwell equations under the Coulomb gauge. Introducing a…
The Poisson problem consists in finding an immersed surface $\Sigma\subset\mathbb{R}^m$ minimising Germain's elastic energy (known as Willmore energy in geometry) with prescribed boundary, boundary Gauss map and area which constitutes a…
We present a continuation of our theoretical research into the influence of co-solvent polarizability on a differential capacitance of the electric double layer [EPL 111, 28002 (2015)]. We formulate a modified Poisson-Boltzmann theory,…
We investigate the statistical mechanics of an inhomogeneous Coulomb fluid composed of charged particles with static polarizability. We derive the weak- and the strong-coupling approximations and evaluate the partition function in a planar…
Singular charge sources in terms of Dirac delta functions present a well-known numerical challenge for solving Poisson's equation. For a sharp interface between inhomogeneous media, singular charges could be analytically treated by…
We propose a novel deterministic particle method to numerically approximate the Landau equation for plasmas. Based on a new variational formulation in terms of gradient flows of the Landau equation, we regularize the collision operator to…
We have obtained the solutions of linearized Shr{\"o}dinger equation for spherically and axially symmetrical electrons density oscillations in plasma in the approximation of the self-consistent field. It was shown that in the center or on…
Solvation effect might have a tremendous influence on chemical reactions. However, precise quantum chemistry calculations are most often done either in vacuum neglecting the role of the solvent or using continuum solvent model ignoring its…
We investigate conformal relative equilibria for Hamiltonian systems on exact Poisson manifolds equipped with scaling symmetries. By introducing conformally Poisson actions and conformal momentum maps, we characterize these equilibria…
We present a general method for determining screened Coulomb parameters in molecular assemblies, in particular organic molecular crystals. This allows us to calculate the interaction parameters used in a generalized Hubbard model…
Classical atomistic simulations based on interatomic potentials resolve lattice instabilities, defect nucleation, and microstructure evolution with high fidelity, but their accessible system sizes remain far below those required for…