Spatial-Order Hierarchy of Time-Dependent Exchange-Correlation Potential

Abstract:Exact time-dependent density-functional theory separates the exchange-correlation potential into interaction and kinetic-correlation components, but the structural relation between them remains unknown. We establish a representability constraint based on the off-diagonal expansion of the one-electron reduced density matrix relative to a time-dependent Hartree-Fock (TDHF) reference. A non-zero linear term generates a non-HF current density while the kinetic-correlation component remains HF representable; higher-order off-diagonal structure activates the kinetic component. In a one-dimensional two-electron correlation quench, retaining the exact interaction component while setting the kinetic component to zero suppresses the density broadening of the exact evolution. These results establish a hierarchy of density equations of motion and provide an exact constraint for non-adiabatic functional construction.

Quantum Physics (quant-ph); Computational Physics (physics.comp-ph)

arXiv:2608.01483 [quant-ph]

(or arXiv:2608.01483v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2608.01483 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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