A Kohn-Sham system at zero temperature

Horia Cornean; K. Hoke; H. Neidhardt; P.N. Racec; J. Rehberg

doi:10.1088/1751-8113/41/38/385304

A Kohn-Sham system at zero temperature

Horia Cornean, K. Hoke, H. Neidhardt, P.N. Racec, J. Rehberg

Institut for Matematiske Fag

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › peer review

4 Citationer (Scopus)

Abstract

A one-dimensional Kohn-Sham system for spin particles is considered which effectively describes semiconductor nanostructures, and which is investigated at zero temperature. We prove the existence of solutions and derive a priori estimates. For this purpose we find estimates for eigenvalues of the Schrödinger operator with effective Kohn-Sham potential and obtain W^1,2-bounds of the associated particle density operator. Afterwards, compactness and continuity results allow us to apply Schauder's fixed point theorem. In the case of vanishing exchange-correlation potential uniqueness is shown by monotonicity arguments. Finally, we investigate the behavior of the system if the temperature approaches zero.
Udgivelsesdato: SEP 26

Originalsprog	Engelsk
Tidsskrift	Journal of Physics A: Mathematical and Theoretical (Print Edition)
Vol/bind	41
Udgave nummer	38
Antal sider	21
ISSN	1751-8113
DOI	https://doi.org/10.1088/1751-8113/41/38/385304
Status	Udgivet - 2008

Adgang til dokumentet

10.1088/1751-8113/41/38/385304

AUB Link

Søg efter materialet i Aalborg Universitetsbiblioteks søgemaskine

Citationsformater

@article{043b9e707d7311dd8b88000ea68e967b,

title = "A Kohn-Sham system at zero temperature",

abstract = "A one-dimensional Kohn-Sham system for spin particles is considered which effectively describes semiconductor nanostructures, and which is investigated at zero temperature. We prove the existence of solutions and derive a priori estimates. For this purpose we find estimates for eigenvalues of the Schr{\"o}dinger operator with effective Kohn-Sham potential and obtain W1,2-bounds of the associated particle density operator. Afterwards, compactness and continuity results allow us to apply Schauder's fixed point theorem. In the case of vanishing exchange-correlation potential uniqueness is shown by monotonicity arguments. Finally, we investigate the behavior of the system if the temperature approaches zero.",

author = "Horia Cornean and K. Hoke and H. Neidhardt and P.N. Racec and J. Rehberg",

year = "2008",

doi = "10.1088/1751-8113/41/38/385304",

language = "English",

volume = "41",

journal = "Journal of Physics A: Mathematical and Theoretical (Print Edition)",

issn = "1751-8113",

publisher = "IOP Publishing",

number = "38",

}

TY - JOUR

T1 - A Kohn-Sham system at zero temperature

AU - Cornean, Horia

AU - Hoke, K.

AU - Neidhardt, H.

AU - Racec, P.N.

AU - Rehberg, J.

PY - 2008

Y1 - 2008

N2 - A one-dimensional Kohn-Sham system for spin particles is considered which effectively describes semiconductor nanostructures, and which is investigated at zero temperature. We prove the existence of solutions and derive a priori estimates. For this purpose we find estimates for eigenvalues of the Schrödinger operator with effective Kohn-Sham potential and obtain W1,2-bounds of the associated particle density operator. Afterwards, compactness and continuity results allow us to apply Schauder's fixed point theorem. In the case of vanishing exchange-correlation potential uniqueness is shown by monotonicity arguments. Finally, we investigate the behavior of the system if the temperature approaches zero.

AB - A one-dimensional Kohn-Sham system for spin particles is considered which effectively describes semiconductor nanostructures, and which is investigated at zero temperature. We prove the existence of solutions and derive a priori estimates. For this purpose we find estimates for eigenvalues of the Schrödinger operator with effective Kohn-Sham potential and obtain W1,2-bounds of the associated particle density operator. Afterwards, compactness and continuity results allow us to apply Schauder's fixed point theorem. In the case of vanishing exchange-correlation potential uniqueness is shown by monotonicity arguments. Finally, we investigate the behavior of the system if the temperature approaches zero.

U2 - 10.1088/1751-8113/41/38/385304

DO - 10.1088/1751-8113/41/38/385304

M3 - Journal article

SN - 1751-8113

VL - 41

JO - Journal of Physics A: Mathematical and Theoretical (Print Edition)

JF - Journal of Physics A: Mathematical and Theoretical (Print Edition)

IS - 38

ER -

A Kohn-Sham system at zero temperature

Abstract

Adgang til dokumentet

AUB Link

Fingeraftryk

Citationsformater