Reduced Density Matrix Functional Theory And A Reduced Formulation Of Density Functional Theory
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| Format: | Preprint |
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2025
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| _version_ | 1866915706060144640 |
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| author | Fredheim, Håkon R. Kvaal, Simen |
| author_facet | Fredheim, Håkon R. Kvaal, Simen |
| contents | A mathematical framework for reduced density matrix functional theory (RDMFT) is proposed. The work is inspired by and generalizes the work by E.H.~Lieb [E.H. Lieb, Int. J. Quant. Chem. 24(1983), pp.243--277] on density-functional theory (DFT). We introduce a Banach space for density matrices with finite kinetic energy. The dual space is a rich class of single-particle potentials, i.e., Hermitian forms. The ground state energy of an $N$-fermion system with external forces given by any such Hermitian form is expressed as the Legendre--Fenchel transform of a convex and lower semicontinuous ``universal'' reduced density matrix functional. The formalism is employed to provide a mathematical framework for density-functional theory (DFT). The main tool here is a rigorous definition of diagonals of reduced density matrices. The result is a refinement of Lieb's results on DFT applicable to a wide variety of models. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_12242 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Reduced Density Matrix Functional Theory And A Reduced Formulation Of Density Functional Theory Fredheim, Håkon R. Kvaal, Simen Mathematical Physics Chemical Physics A mathematical framework for reduced density matrix functional theory (RDMFT) is proposed. The work is inspired by and generalizes the work by E.H.~Lieb [E.H. Lieb, Int. J. Quant. Chem. 24(1983), pp.243--277] on density-functional theory (DFT). We introduce a Banach space for density matrices with finite kinetic energy. The dual space is a rich class of single-particle potentials, i.e., Hermitian forms. The ground state energy of an $N$-fermion system with external forces given by any such Hermitian form is expressed as the Legendre--Fenchel transform of a convex and lower semicontinuous ``universal'' reduced density matrix functional. The formalism is employed to provide a mathematical framework for density-functional theory (DFT). The main tool here is a rigorous definition of diagonals of reduced density matrices. The result is a refinement of Lieb's results on DFT applicable to a wide variety of models. |
| title | Reduced Density Matrix Functional Theory And A Reduced Formulation Of Density Functional Theory |
| topic | Mathematical Physics Chemical Physics |
| url | https://arxiv.org/abs/2510.12242 |