Time-dependent Thomas-Fermi

Domps, A., Reinhard, P.-G. and Suraud, E. (1998). Time-dependent Thomas-Fermi approach to electron dynamics in metal clusters, Phys. Rev. Lett. 80, 5520-5523. 

Time-dependent density functional theory (TDDFT) as a complete formalism [7] is a more recent development, although the historical roots date back to the time-dependent Thomas-Fermi model proposed by Bloch [8] as early as 1933. The first and rather successful steps towards a time-dependent Kohn-Sham (TDKS) scheme were taken by Peuckert [9] and by Zangwill and Soven [10]. These authors treated the linear density response of rare-gas atoms to a time-dependent external potential as the response of non-interacting electrons to an effective time-dependent potential. In analogy to stationary KS theory, this effective potential was assumed to contain an exchange-correlation (xc) part, r,c(r, t), in addition to the time-dependent external and Hartree terms ... 

In addition, there is interest in further extending the discussion to a variety of situations, that have recently gained much attention in the nonrelativistic case, as time-dependent systems [49], excited states [45] or finite temperature ensembles [110]. As an example of work along these lines we mention the gradient expansion of the noninteracting, relativistic free energy [110], leading to a temperature-dependent relativistic extended Thomas-Fermi model. 

This method has been successfully applied to the photoionization of Hg and Xe [103,101] as well as to the evaluation of the polarizabilities of heavy closed-shell atoms [104] (using a direct time-dependent extension of the LDA for the xc-functional). A concept to deal with excited states in the framework of RDFT has been put forward by Nagy [105]. The derivation and first applications of relativistic extended Thomas-Fermi models may be found in Refs.[106-112]. Furthermore, an RDFT approach to meson field theory for hadronic matter (quantum hadrodynamics) [113] has been established by Speicher et al. [114]. This hadronic RDFT has been successfully applied to the description of nuclear ground states both within the extended Thomas-Fermi model [115-118] and within the KS scheme [119-121]. A corresponding formalism for finite temperature is also available [122,123]. 

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