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Related Experiment Videos

Time-dependent V-representability on lattice systems.

Yonghui Li1, C A Ullrich

  • 1Department of Physics and Astronomy, University of Missouri, Columbia, Missouri 65211, USA.

The Journal of Chemical Physics
|August 7, 2008
PubMed
Summary
This summary is machine-generated.

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Discretization of electronic systems on lattices breaks the link between time-dependent densities and potentials. This study reveals issues with the continuity equation, impacting time-dependent density-functional theory applications.

Area of Science:

  • Computational Physics
  • Quantum Chemistry
  • Materials Science

Background:

  • The relationship between time-dependent densities and potentials is fundamental in electronic structure theory.
  • Time-dependent density-functional theory (TDDFT) offers a computationally efficient approach to study electronic dynamics.
  • V-representability ensures that a given density can be generated by a valid potential.

Purpose of the Study:

  • To investigate the mapping between time-dependent densities and potentials for noninteracting electronic systems on lattices.
  • To analyze the breakdown of time-dependent V-representability in discretized systems.
  • To discuss the implications for numerical implementations of TDDFT.

Main Methods:

  • Analysis of the continuity equation for noninteracting electronic systems on lattices.

Related Experiment Videos

  • Examination of lattice models with two and N points.
  • Comparison with the continuum limit.

    • Main Results:

    • Identified specific time-dependent density functions on lattices that lack a corresponding real time-dependent potential.
    • Attributed the loss of time-dependent V-representability to discretization-induced problems in the continuity equation.
    • Demonstrated that time-dependent noninteracting V-representability is recovered in the continuum limit.

    Conclusions:

    • Discretization of the kinetic-energy operator on lattices poses challenges for time-dependent V-representability in electronic systems.
    • Numerical applications of TDDFT may encounter limitations due to these lattice artifacts.
    • The continuum limit is crucial for restoring the fundamental mapping between densities and potentials.