# 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.

## 7 Citations

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

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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

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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 the reduced Hartree-Fock equations with a Small Anderson Type Background Charge Distribution

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### On Capacitance and Energy Storage of Supercapacitor with Dielectric Constant Discontinuity

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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

- PhysicsMolecular Physics
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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

- Materials ScienceColloid Journal
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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…

### Automatic 3D cluster modelling of COVID-19 through voxel-based redistribution

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## References

SHOWING 1-10 OF 37 REFERENCES

### Solutions of Hartree-Fock equations for Coulomb systems

- Mathematics
- 1987

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

- PhysicsTrends in Mathematics
- 2019

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

- Mathematics
- 1977

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

- MathematicsArchive 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

- Mathematics
- 1993

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

- Physics, MathematicsJournal of Evolution Equations
- 2022

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

- Physics
- 2012

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

- Mathematics
- 2010

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…