Solver for the Electronic V-Representation Problem of Time-Dependent Density Functional Theory

Area of Science:

• Quantum Mechanics
• Computational Chemistry
• Theoretical Physics

Background:

• Time-dependent density functional theory (TDDFT) is crucial for numerically simulating quantum systems.
• The accuracy of TDDFT relies on V-representability, a concept previously explored.
• Efficient numerical methods are needed for accurate quantum system propagation.

Purpose of the Study:

• To introduce a novel solver for the scalar time-dependent Kohn-Sham potential.
• To analyze the force-balance equation underpinning the numerical method.
• To present new insights into V-representability for one-electron systems.

Main Methods:

• Development of a new numerical solver for the time-dependent Kohn-Sham potential.
• Implementation of a force-balance equation for numerical propagation.
• Utilizing preconditioning for matrix inversion and self-consistent potential calculation.
• Testing on one- and two-electron systems in 1D and 3D grids.

Main Results:

• Successful implementation and testing of the new TDDFT solver.
• Illustrative numerical results demonstrating the method's efficacy for small quantum systems.
• Presentation of a new characterization of V-representability for one-electron systems.

Conclusions:

• The developed solver offers an improved approach for propagating quantum systems using TDDFT.
• The numerical innovations enhance the accuracy and efficiency of quantum dynamics simulations.
• Further research directions include exploring more complex systems and refining V-representability analysis.