The Dirac–Frenkel principle for reduced density matrices and the Bogoliubov–de Gennes equations

Benedikter, Niels and Sok, Jérémy and Solovej, Jan P (2018) The Dirac–Frenkel principle for reduced density matrices and the Bogoliubov–de Gennes equations. Annales Henri Poincare, 19 (4). 1167-1214 . ISSN 1424-0661

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Official URL: http://dx.doi.org/10.1007/s00023-018-0644-z

Abstract

The derivation of effective evolution equations is central to the study of non-stationary quantum many-body systems, and widely used in contexts such as superconductivity, nuclear physics, Bose–Einstein condensation and quantum chemistry. We reformulate the Dirac–Frenkel approximation principle in terms of reduced density matrices and apply it to fermionic and bosonic many-body systems. We obtain the Bogoliubov–de Gennes and Hartree–Fock–Bogoliubov equations, respectively. While we do not prove quantitative error estimates, our formulation does show that the approximation is optimal within the class of quasifree states. Furthermore, we prove well-posedness of the Bogoliubov–de Gennes equations in energy space and discuss conserved quantities.

Item Type: Article
DOI: 10.1007/s00023-018-0644-z
Subjects: 500 Science > 510 Mathematics
500 Science > 530 Physics > 539 Modern physics
Research Group: Seiringer Group
SWORD Depositor: Sword Import User
Depositing User: Sword Import User
Date Deposited: 03 Apr 2018 07:31
Last Modified: 03 Apr 2018 07:31
URI: https://repository.ist.ac.at/id/eprint/993

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