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Stochastic time-dependent current-density-functional theory.

Massimiliano Di Ventra1, Roberto D'Agosta

  • 1University of California-San Diego, La Jolla, California 92093, USA. diventra@physics.ucsd.edu

Physical Review Letters
|August 7, 2007
PubMed
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A new time-dependent current-density-functional theory is developed for open quantum systems. This theory proves that identical current densities imply identical external potentials, enabling new calculations beyond standard quantum dynamics.

Area of Science:

  • Quantum Mechanics
  • Condensed Matter Physics
  • Computational Chemistry

Background:

  • Current-density-functional theory (DFT) is a powerful tool for studying many-particle systems.
  • Extending DFT to open quantum systems interacting with external baths remains a significant challenge.
  • Existing methods often struggle to accurately describe time evolution beyond conservative Hamiltonian dynamics.

Purpose of the Study:

  • To develop a time-dependent current-density-functional theory (TDCDFT) applicable to open quantum systems.
  • To establish a theoretical framework for calculating the time evolution of many-particle systems interacting with arbitrary external baths.
  • To expand the applicability of TDDFT to systems beyond isolated, conservative dynamics.

Main Methods:

  • Development of a novel time-dependent current-density-functional theory framework.

Related Experiment Videos

  • Mathematical proof demonstrating the uniqueness of external potentials for a given current density.
  • Utilizing ensemble-averaged current density, j(r,t), as the fundamental quantity.

    • Main Results:

    • A rigorous proof shows that two external vector potentials yielding the same ensemble-averaged current density must be equivalent up to a gauge transformation.
    • The developed TDCDFT is applicable to many-particle systems interacting with arbitrary external baths.
    • The theory enables first-principles calculations of many-particle time evolution beyond traditional Hamiltonian dynamics.

    Conclusions:

    • The developed TDCDFT significantly expands the scope of density-functional theory to encompass open quantum systems.
    • This work provides a foundation for accurate first-principles simulations of complex quantum dynamics in realistic environments.
    • The findings pave the way for novel computational approaches in condensed matter physics and quantum chemistry.