- Title Pages
- Preface
- List of abbreviations
- 1 Introduction
- 2 Review of ground-state density-functional theory
- 3 Fundamental existence theorems
- 4 The time-dependent Kohn–Sham scheme
- 5 Time-dependent observables
- 6 Properties of the time-dependent xc potential
- 7 The formal framework of linear-response TDDFT
- 8 The frequency-dependent xc kernel
- 9 Applications to atomic and molecular systems
- 10 Time-dependent current-DFT
- 11 The time-dependent optimized effective potential
- 12 Extended systems
- 13 TDDFT and many-body theory
- 14 Long–range correlations and dispersion interactions
- 15 Nanoscale transport and molecular junctions
- 16 Strong-field phenomena and optimal control
- 17 Nuclear motion
- Appendix A Atomic units
- Appendix B Functionals and functional derivatives
- Appendix C Densities and density matrices
- Appendix D Hartree–Fock and other wave-function approaches
- Appendix E Constructing the xc potential from a given density
- Appendix F DFT for excited states
- Appendix G Systems with noncollinear spins
- Appendix H The dipole approximation
- Appendix I A brief review of classical fluid dynamics
- Appendix J Constructing the scalar xc kernel from the tensor xc kernel
- Appendix K Semiconductor quantum wells
- Appendix L TDDFT in a Lagrangian frame
- Appendix M Inversion of the dielectric matrix
- Appendix N Review literature on DFT and many-body theory
- Appendix O TDDFT computer codes
- References
- Index

# Time-dependent current-DFT

# Time-dependent current-DFT

- Chapter:
- (p.213) 10 Time-dependent current-DFT
- Source:
- Time-Dependent Density-Functional Theory
- Author(s):
### Carsten A. Ullrich

- Publisher:
- Oxford University Press

This chapter discusses time-dependent current-density-functional theory (TDCDFT). It first asks under what circumstances one should choose the current density as basic variable, instead of the particle density. There are several reasons: a current-based formulation is more suitable for constructing functionals beyond the adiabatic approximation. Furthermore, the current is the natural variable to describe coupling to electromagnetic fields and vector potentials. The basic existence theorems of TDCDFT are proved, and several exact properties and the linear-response regime are discussed. The second half of the chapter deals with the so-called Vignale-Kohn functional, which is a local and frequency-dependent approximation to the exchange-correlation vector potential. The Vignale-Kohn functional is expressed in terms of viscoelastic stresses in the electron liquid. Several applications in the linear-response regime and in real time are presented. The Vignale-Kohn functional works well for describing dissipative effects in collective, plasmon-like electron dynamics.

*Keywords:*
time-dependent current-density-functional theory, basic variable, linear-response regime, Vignale-Kohn functional, adiabatic approximation, viscoelastic stresses

Oxford Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us .

- Title Pages
- Preface
- List of abbreviations
- 1 Introduction
- 2 Review of ground-state density-functional theory
- 3 Fundamental existence theorems
- 4 The time-dependent Kohn–Sham scheme
- 5 Time-dependent observables
- 6 Properties of the time-dependent xc potential
- 7 The formal framework of linear-response TDDFT
- 8 The frequency-dependent xc kernel
- 9 Applications to atomic and molecular systems
- 10 Time-dependent current-DFT
- 11 The time-dependent optimized effective potential
- 12 Extended systems
- 13 TDDFT and many-body theory
- 14 Long–range correlations and dispersion interactions
- 15 Nanoscale transport and molecular junctions
- 16 Strong-field phenomena and optimal control
- 17 Nuclear motion
- Appendix A Atomic units
- Appendix B Functionals and functional derivatives
- Appendix C Densities and density matrices
- Appendix D Hartree–Fock and other wave-function approaches
- Appendix E Constructing the xc potential from a given density
- Appendix F DFT for excited states
- Appendix G Systems with noncollinear spins
- Appendix H The dipole approximation
- Appendix I A brief review of classical fluid dynamics
- Appendix J Constructing the scalar xc kernel from the tensor xc kernel
- Appendix K Semiconductor quantum wells
- Appendix L TDDFT in a Lagrangian frame
- Appendix M Inversion of the dielectric matrix
- Appendix N Review literature on DFT and many-body theory
- Appendix O TDDFT computer codes
- References
- Index