On the "Causality Paradox" of Time-Dependent Density Functional Theory

Abstract

I show that the so-called causality paradox of time-dependent density functional theory arises from an incorrect formulation of the variational principle for the time evolution of the density. The correct formulation not only resolves the paradox in real time, but also leads to a new expression for the causal exchange-correlation kernel in terms of Berry curvature. Furthermore, I show that all the results that were previously derived from symmetries of the action functional remain valid in the present formulation. Finally, I develop a model functional theory which explicitly demonstrates the workings of the new formulation.

21 pages

References in corpus (6)

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• Is time-dependent density functional theory formally exact?
• Quantum many-body dynamics in a Lagrangian frame: II. Geometric formulation of time-dependent density functional theory
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Cited by in corpus (39)

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• A stochastic approach to open quantum systems
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• Non-Adiabatic Approximations in Time-Dependent Density Functional Theory: Progress and Prospects
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• Local-in-time error in variational quantum dynamics
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• Force Balance Approach for Advanced Approximations in Density Functional Theories
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• Nonlocal and nonadiabatic Pauli potential for time-dependent orbital-free density functional theory
• Time-dependent current density functional theory via time-dependent deformation functional theory: A constrained search formulation in the time domain
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• Excitation Energies from Thermally-Assisted-Occupation Density Functional Theory: Theory and Computational Implementation
• Time-Dependent Multi-Component Density Functional Theory for Coupled Electron-Positron Dynamics
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• Modifying the variational principle in the action integral functional derivation of time-dependent density functional theory
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• Comment on "Modifying the variational principle in the action integral functional derivation of time-dependent density functional theory" by Jochen Schirmer [arXiv:1010.4223]
• Energy densities in quantum mechanics
• Time-dependent density functional theory for X-ray near-edge spectroscopy
• Nonlocal Orbital-Free Kinetic Energy Functional from the Jellium-with-Gap Model for Finite Systems
• Wick rotation derivation for weak values of the density and time-dependent density functional theory
• Kohn-Sham scheme for frequency dependent linear response
• Brief review related to the foundations of time-dependent density functional theory