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We extended the Van Leeuwen theorem for time-dependent density functional theory (TDDFT) to accurately reconstruct multibody density evolution. This provides a unique nonlocal potential for correlated systems, improving predictions for kinetic processes.

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Area of Science:

  • Quantum mechanics
  • Computational physics
  • Theoretical chemistry

Background:

  • Time-dependent density functional theory (TDDFT) is crucial for predicting material properties.
  • The Van Leeuwen theorem ensures unique potentials for one-body density evolution in TDDFT.
  • Existing TDDFT methods face challenges in accurately describing multibody interactions and complex dynamics.

Purpose of the Study:

  • To generalize the Van Leeuwen theorem by exploring truncation criteria in the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy.
  • To develop a unique nonlocal potential for accurately reconstructing multibody density evolution in interacting systems.
  • To extend the capabilities of TDDFT for describing complex kinetic processes in correlated systems.

Main Methods:

  • Exploration of truncation criteria within the BBGKY hierarchy.
  • Development of a generalized Van Leeuwen theorem for multibody systems.
  • Construction of a static many-body potential and extension of the Casida equation.

Main Results:

  • Demonstration of a unique nonlocal potential for accurate multibody density evolution reconstruction.
  • Validation of BBGKY hierarchy truncation for consistent reduced equation behavior.
  • Successful extension of the Casida equation for multiple-excitation energy calculations.

Conclusions:

  • The extended TDDFT framework offers an accurate, first-principles approach for correlated systems.
  • This work enhances the description of kinetic processes, including particle transport, multiple excitations, and ionization.
  • The generalized theorem provides a robust foundation for future advancements in TDDFT applications.