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


Author(s): Benedikter, Niels; Sok, Jérémy; Solovej, Jan P
Article Title: The Dirac–Frenkel principle for reduced density matrices and the Bogoliubov–de Gennes equations
Title Series: Annales Henri Poincare
Affiliation IST Austria
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
Journal Title: Annales Henri Poincare
Volume: 19
Issue 4
ISSN: 1424-0661
Publisher: Birkhäuser  
Date Published: 2018-04-01
Start Page: 1167
End Page: 1214
Copyright Statement: CC BY
URL:
DOI: 10.1007/s00023-018-0644-z
Notes: Open access funding provided by Institute of Science and Technology (IST Austria). The authors acknowledge support by ERC Advanced Grant 321029 and by VILLUM FONDEN via the QMATH Centre of Excellence (Grant No. 10059). The authors would like to thank Sébastien Breteaux, Enno Lenzmann, Mathieu Lewin and Jochen Schmid for comments and discussions about well-posedness of the Bogoliubov–de Gennes equations.
Open access: yes (OA journal)
IST Austria Authors