Is time-dependent density functional theory formally exact?
| dc.creator | Schirmer, J. | |
| dc.creator | Dreuw, A. | |
| dc.date | 2006-02-01 | |
| dc.date | 2006-04-03 | |
| dc.date.accessioned | 2026-07-07T08:23:12Z | |
| dc.date.available | 2026-07-07T08:23:12Z | |
| dc.description | The general expectation that, in principle, time-dependent density functional theory (TDDFT) be an exact formulation of the time-evolution of an interacting N-electron system is critically reexamined. It is demonstrated that the previous TDDFT foundation, resting on three theorems by Runge and Gross (RG) [Phys.Rev.Lett.52, 997(1984)], is invalid because undefined phase factors corrupt the RG action integral functionals. Our finding confirms much of a previous analysis by van Leeuwen [Int. J. Mod. Phys. B15, 1969(2001)]. To analyze the RG theorems and other aspects of TDDFT, an utmost simplification of the KS theory is introduced, in which the density is obtained from a single KS equation for one spatial (spin-less) particle. This radical KS formulation allows us to analyze also the concept of KS-type equations derived without a variational principle. We argue that such an approach can reproduce, but not predict the time-development of the exact density of the interacting N-electron system. Besides the issue of the formal exactness of TDDFT, it is shown that both the static and time-dependent KS linear response equations neglect the particle-particle (p-p) and hole-hole (h-h) matrix elements of the perturbing operator. For a local (multiplicative) operator this does not lead to a loss of information due to a remarkable general property of local operators. Accordingly, no logical inconsistency arises here, because DFT requires external potentials to be local. | |
| dc.description | Reason for replacement: Change of content essentially in subsection 5.C, plus minor adaptions in the Appendix, Sec. 1, and Sec. 6 | |
| dc.identifier | https://arxiv.org/abs/cond-mat/0602020 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/0602020 | |
| dc.identifier | Phys. Rev. A 75, 022513 (2007) | |
| dc.identifier | doi:10.1103/PhysRevA.75.022513 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/135908 | |
| dc.subject | Other Condensed Matter | |
| dc.title | Is time-dependent density functional theory formally exact? | |
| dc.type | text |