Floquet theory provides insight into the inversion of time-dependent Kohn-Sham density functional theory. Specifically, mathematical derivations show that the fundamental frequencies of a time-dependent wavefunction solution are the leading-order harmonics for the TD-KS state. Numerical tests of the resulting ansatz in 1D and 3D for atomic and molecular cases demonstrate its utility. In particular, low $L_{2}$ errors in the time-dependent density and longitudinal current were found, even though currents were not an explicit optimization objective. In all, the proposed inversion ansatz provides exchange-correlation potentials from time-dependent wavefunctions, is highly interpretable, and may significantly help in the development of nonadiabatic density functionals.Floquet theory provides insight into the inversion of time-dependent Kohn-Sham density functional theory. Specifically, mathematical derivations show that the fundamental frequencies of a time-dependent wavefunction solution are the leading-order harmonics for the TD-KS state. Numerical tests of the resulting ansatz in 1D and 3D for atomic and molecular cases demonstrate its utility. In particular, low $L_{2}$ errors in the time-dependent density and longitudinal current were found, even though currents were not an explicit optimization objective. In all, the proposed inversion ansatz provides exchange-correlation potentials from time-dependent wavefunctions, is highly interpretable, and may significantly help in the development of nonadiabatic density functionals.

arXiv:2609.34164Sep 28, 20260 citations

Quantum-mechanical interpretation of time-dependent density-functional theory

Zhixin Qian, Viraht Sahni

Physics Letters AOct 1, 199829 citations

Quantal Density Functional Theory of Degenerate States

Viraht Sahni, Xiao‐Yin Pan

The treatment of degenerate states within Kohn-Sham density functional theory is a problem of long-standing and current interest. We propose a solution to this mapping from the interacting degenerate system to that of the noninteracting fermion model whereby the equivalent density and energy are obtained via the unifying physical framework of quantal density functional theory. We describe the quantal theory of both ground and excited degenerate states, and for the cases of both pure state and ensemble v-representable densities. The quantal description further provides a rigorous physical interpretation of the corresponding Kohn-Sham energy functionals of the density, ensemble density, bidensity and ensemble bidensity, and of their respective functional derivatives. We conclude with examples of the mappings within the quantal theory.The treatment of degenerate states within Kohn-Sham density functional theory is a problem of long-standing and current interest. We propose a solution to this mapping from the interacting degenerate system to that of the noninteracting fermion model whereby the equivalent density and energy are obtained via the unifying physical framework of quantal density functional theory. We describe the quantal theory of both ground and excited degenerate states, and for the cases of both pure state and ensemble v-representable densities. The quantal description further provides a rigorous physical interpretation of the corresponding Kohn-Sham energy functionals of the density, ensemble density, bidensity and ensemble bidensity, and of their respective functional derivatives. We conclude with examples of the mappings within the quantal theory.

arXiv:cond-mat/0210129Physical Review LettersMar 27, 200328 citations

Relaxation in Time-Dependent Current-Density-Functional Theory

Roberto D’Agosta, Giovanni Vignale

We apply the time-dependent current-density-functional theory to the study of the relaxation of a closed many-electron system evolving from a nonequilibrium initial state. We show that the self-consistent unitary time evolution generated by the exchange-correlation vector potential irreversibly drives the system to equilibrium. We also show that the energy dissipated in the Kohn-Sham system, i.e., the noninteracting system whose particle and current densities coincide with those of the physical system under study, is related to the entropy production in the real system.We apply the time-dependent current-density-functional theory to the study of the relaxation of a closed many-electron system evolving from a nonequilibrium initial state. We show that the self-consistent unitary time evolution generated by the exchange-correlation vector potential irreversibly drives the system to equilibrium. We also show that the energy dissipated in the Kohn-Sham system, i.e., the noninteracting system whose particle and current densities coincide with those of the physical system under study, is related to the entropy production in the real system.

arXiv:cond-mat/0508175Physical Review LettersJan 11, 200647 citations

L_{2}

errors in the time-dependent density and longitudinal current were found, even though currents were not an explicit optimization objective. In all, the proposed inversion ansatz provides exchange-correlation potentials from time-dependent wavefunctions, is highly interpretable, and may significantly help in the development of nonadiabatic density functionals.