On derivation of the Poisson-Boltzmann equation

DOI10.1007/s10955-020-02562-8zbMath1448.35110arXiv2012.02326OpenAlexW3113251694MaRDI QIDQ2194194

Publication date: 25 August 2020

Published in: Journal of Statistical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2012.02326

zbMATH Keywords

density functional theory electrostatics Poisson-Boltzmann equation Kohn-Sham equation microscopic limit partial differential equations of quantum physics

Mathematics Subject Classification ID

Electromagnetic interaction; quantum electrodynamics (81V10) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Boltzmann equations (35Q20) Equilibrium statistical mechanics (82Bxx)

Related Items (2)

On an effective equation of the reduced Hartree-Fock theory ⋮ On the reduced Hartree-Fock equations with a small Anderson type background charge distribution

Cites Work

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The electronic structure of smoothly deformed crystals: Wannier functions and the Cauchy-Born Rule
Existence of atoms and molecules in the mean-field approximation of no-photon quantum electrodynamics
The dielectric permittivity of crystals in the reduced Hartree-Fock approximation
A new approach to the modeling of local defects in crystals: The reduced Hartree-Fock case
Existence of minimizers for Kohn-Sham models in quantum chemistry
Expectations and entropy inequalities for finite quantum systems
Existence and nonlinear stability of stationary states of the Schrödinger-Poisson system
On some periodic Hartree-type models for crystals
Solutions of Hartree-Fock equations for Coulomb systems
On the Kohn-Sham equations with periodic background potentials
Generalized Hartree-Fock theory and the Hubbard model
A mathematical formulation of the random phase approximation for crystals
On effective PDEs of quantum physics
Effective Maxwell equations from time-dependent density functional theory
The Microscopic Origin of the Macroscopic Dielectric Permittivity of Crystals: A Mathematical Viewpoint
A variational formulation of schrödinger-poisson systems in dimension d ≤ 3
Kernels of Trace Class Operators
The stability of matter: from atoms to stars
Electronic structure of smoothly deformed crystals: Cauchy-born rule for the nonlinear tight-binding model
The Kohn-Sham equation for deformed crystals
From atoms to crystals: a mathematical journey
Mathematical concepts of quantum mechanics.
On the thermodynamic limit for Hartree-Fock type models

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