Orbitally stable states in generalized Hartree-Fock theory

Jean Dolbeault; Patricio Felmer; Mathieu Lewin

doi:10.1142/S0218202509003450

Orbitally stable states in generalized Hartree-Fock theory

Jean Dolbeault
, Patricio Felmer
, Mathieu Lewin

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

Abstract

This paper is devoted to a generalized Hartree-Fock model in the Euclidean space. For large classes of free energy functionals, minimizers are obtained as long as the total charge of the system does not exceed a threshold which depends on a parameter that we call the temperature in analogy with models based on a thermodynamical approach. The usual Hartree-Fock model is recovered in the zero temperature limit. An orbital stability result for the Cauchy problem is deduced from the variational approach.

Original language	English
Pages (from-to)	347-367
Number of pages	21
Journal	Mathematical Models and Methods in Applied Sciences
Volume	19
Issue number	3
DOIs	https://doi.org/10.1142/S0218202509003450
Publication status	Published - 1 Jan 2009
Externally published	Yes

Keywords

Asymptotic distribution of eigenvalues
Compact self-adjoint operators
Entropy
Free energy
HartreeFock model
LiebThirring inequality
Mixed states
Occupation numbers
Schrödinger operator
Self-consistent potential
Temperature
Trace-class operators

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10.1142/S0218202509003450

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abstract = "This paper is devoted to a generalized Hartree-Fock model in the Euclidean space. For large classes of free energy functionals, minimizers are obtained as long as the total charge of the system does not exceed a threshold which depends on a parameter that we call the temperature in analogy with models based on a thermodynamical approach. The usual Hartree-Fock model is recovered in the zero temperature limit. An orbital stability result for the Cauchy problem is deduced from the variational approach.",

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AU - Felmer, Patricio

AU - Lewin, Mathieu

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N2 - This paper is devoted to a generalized Hartree-Fock model in the Euclidean space. For large classes of free energy functionals, minimizers are obtained as long as the total charge of the system does not exceed a threshold which depends on a parameter that we call the temperature in analogy with models based on a thermodynamical approach. The usual Hartree-Fock model is recovered in the zero temperature limit. An orbital stability result for the Cauchy problem is deduced from the variational approach.

AB - This paper is devoted to a generalized Hartree-Fock model in the Euclidean space. For large classes of free energy functionals, minimizers are obtained as long as the total charge of the system does not exceed a threshold which depends on a parameter that we call the temperature in analogy with models based on a thermodynamical approach. The usual Hartree-Fock model is recovered in the zero temperature limit. An orbital stability result for the Cauchy problem is deduced from the variational approach.

KW - Asymptotic distribution of eigenvalues

KW - Compact self-adjoint operators

KW - Entropy

KW - Free energy

KW - HartreeFock model

KW - LiebThirring inequality

KW - Mixed states

KW - Occupation numbers

KW - Schrödinger operator

KW - Self-consistent potential

KW - Temperature

KW - Trace-class operators

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EP - 367

JO - Mathematical Models and Methods in Applied Sciences

JF - Mathematical Models and Methods in Applied Sciences

IS - 3

ER -

Orbitally stable states in generalized Hartree-Fock theory

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Keywords

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