On Derivation of the Poisson–Boltzmann Equation

@article{Chenn2020OnDO,
  title={On Derivation of the Poisson–Boltzmann Equation},
  author={Ilias Chenn and Israel Michael Sigal},
  journal={Journal of Statistical Physics},
  year={2020},
  volume={180},
  pages={954-1001}
}
Starting from the microscopic reduced Hartree–Fock equation, we derive the macroscopic linearized Poisson–Boltzmann equation for the electrostatic potential associated with the electron density. 

On the Reduced Hartree-Fock Equation with Anderson Type Background Charge Distribution

We demonstrate that the reduced Hartree-Fock equation (REHF) with an Anderson type background charge distribution has an unique stationary solution by explicitly computing a screening mass at

On a Novel Effective Equation of the Reduced Hartree-Fock Theory

We show that there is an one-to-one correspondence between solutions to the Poisson-Landscape equations and the reduced Hartree-Fock equations in the semi-classical limit at low temperature.

On Capacitance and Energy Storage of Supercapacitor with Dielectric Constant Discontinuity

The classical density functional theory (CDFT) is applied to investigate influences of electrode dielectric constant on specific differential capacitance Cd and specific energy storage E of a

Effective electrostatic forces between two neutral surfaces with surface charge separation: valence asymmetry and dielectric constant heterogeneity

  • S. Zhou
  • Physics
    Molecular Physics
  • 2022
Based on CDFT calculations, we study new features of surface electrostatic force (SEF) between two face-to-face overall neutral surfaces, each of which is comprised of atomic scale strip shape charge

Analytical Solution of Modified Poisson–Boltzmann Equation and Application to Cylindrical Nanopore Supercapacitor Energy Storage

Abstract An approximate and analytical solution is obtained for a modified Poisson−Boltzmann (MPB) equation describing + z /− z electrolyte confined inside a cylindrical pore. Three expressions are

References

SHOWING 1-10 OF 37 REFERENCES

Solutions of Hartree-Fock equations for Coulomb systems

This paper deals with the existence of multiple solutions of Hartree-Fock equations for Coulomb systems and related equations such as the Thomas-Fermi-Dirac-Von Weizäcker equation.

On Effective PDEs of Quantum Physics

The Hartree-Fock equation is a key effective equation of quantum physics. We review the standard derivation of this equation and its properties and present some recent results on its natural

The Hartree-Fock theory for Coulomb systems

For neutral atoms and molecules and positive ions and radicals, we prove the existence of solutions of the Hartree-Fock equations which minimize the Hartree-Fock energy. We establish some properties

Screening in the Finite-Temperature Reduced Hartree–Fock Model

  • A. Levitt
  • Mathematics
    Archive for Rational Mechanics and Analysis
  • 2020
We prove the existence of solutions of the reduced Hartree–Fock equations at finite temperature for a periodic crystal with a small defect, and show the total screening of the defect charge by the

A variational formulation of schrödinger-poisson systems in dimension d ≤ 3

This paper is devoted to the analysis of a Schrodinger-Poisson system arising from the modelling of electronic devices. We propose a variational formulation which ensures existence and uniqueness of

The time-dependent Hartree–Fock–Bogoliubov equations for Bosons

We introduce the map of dynamics of quantum Bose gases into dynamics of quasifree states, which we call the “nonlinear quasifree approximation”. We use this map to derive the time-dependent

The Microscopic Origin of the Macroscopic Dielectric Permittivity of Crystals: A Mathematical Viewpoint

The purpose of this paper is to provide a mathematical analysis of the Adler-Wiser formula relating the macroscopic relative permittivity tensor to the microscopic structure of the crystal at the

Electronic structure of smoothly deformed crystals: Cauchy‐born rule for the nonlinear tight‐binding model

The electronic structure of a smoothly deformed crystal is analyzed using a minimalist model in quantum many‐body theory, the nonlinear tight‐binding model. An extension of the classical Cauchy‐Born