Existence of solutions to the Efros self-consistency equation in all dimensions

Yisong Yang

doi:10.1098/rspa.2002.1064

Existence of solutions to the Efros self-consistency equation in all dimensions

Yisong Yang

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper we develop in all dimensions an existence theory for the Efros energy-domain self-consistent equation governing the density of single-electron states. When the energy domain extends to infinity, we prove that solutions exist except in dimension one. When the energy domain is finite, we prove that solutions exist in all dimensions. The boundary condition near the Fermi level makes the integral diverge. Such a difficulty can be overcome by using a perturbed equation as an approximation and then passing to the zero perturbation limit.

Original language	English (US)
Pages (from-to)	853-861
Number of pages	9
Journal	Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume	459
Issue number	2032
DOIs	https://doi.org/10.1098/rspa.2002.1064
State	Published - Apr 8 2003

Keywords

Fixed-point theorem
Nonlinear integral equations
Perturbation

ASJC Scopus subject areas

General Mathematics
General Engineering
General Physics and Astronomy

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10.1098/rspa.2002.1064

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abstract = "In this paper we develop in all dimensions an existence theory for the Efros energy-domain self-consistent equation governing the density of single-electron states. When the energy domain extends to infinity, we prove that solutions exist except in dimension one. When the energy domain is finite, we prove that solutions exist in all dimensions. The boundary condition near the Fermi level makes the integral diverge. Such a difficulty can be overcome by using a perturbed equation as an approximation and then passing to the zero perturbation limit.",

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AB - In this paper we develop in all dimensions an existence theory for the Efros energy-domain self-consistent equation governing the density of single-electron states. When the energy domain extends to infinity, we prove that solutions exist except in dimension one. When the energy domain is finite, we prove that solutions exist in all dimensions. The boundary condition near the Fermi level makes the integral diverge. Such a difficulty can be overcome by using a perturbed equation as an approximation and then passing to the zero perturbation limit.

KW - Fixed-point theorem

KW - Nonlinear integral equations

KW - Perturbation

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JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

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Existence of solutions to the Efros self-consistency equation in all dimensions

Abstract

Keywords

ASJC Scopus subject areas

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