Journal
ANNALES HENRI POINCARE
Volume 19, Issue 4, Pages 1167-1214Publisher
SPRINGER INTERNATIONAL PUBLISHING AG
DOI: 10.1007/s00023-018-0644-z
Keywords
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Funding
- Institute of Science and Technology (IST Austria)
- ERC [321029]
- VILLUM FONDEN via the QMATH Centre of Excellence [10059]
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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.
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