English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

In this review we provide a rigorous and self-contained presentation ofone-body reduced density-matrix (1RDM) functional theory. We do so for the caseof a finite basis set, where density-functional theory (DFT) implicitly becomesa 1RDM functional theory. To avoid non-uniqueness issues we consider the caseof fermionic and bosonic systems at elevated temperature and variable particlenumber, i.e, a grand-canonical ensemble. For the fermionic case the Fock spaceis finite-dimensional due to the Pauli principle and we can provide a rigorous1RDM functional theory relatively straightforwardly. For the bosonic case,where arbitrarily many particles can occupy a single state, the Fock space isinfinite-dimensional and mathematical subtleties (not every hermitianHamiltonian is self-adjoint, expectation values can become infinite, and notevery self-adjoint Hamiltonian has a Gibbs state) make it necessary to imposerestrictions on the allowed Hamiltonians and external non-local potentials. Forsimple conditions on the interaction of the bosons a rigorous 1RDM functionaltheory can be established, where we exploit the fact that due to the finiteone-particle space all 1RDMs are finite-dimensional. We also discuss theproblems arising from 1RDM functional theory as well as DFT formulated for aninfinite-dimensional one-particle space.

One-body reduced density-matrix functional theory in finite basis sets at elevated temperatures