Title 



Some pointers towards a future orbitalfree density functional theory of inhomogeneous electron liquids
 
Author 


  
Abstract 



Recent work by Gaacutel and March has been concerned with a model twoelectron atom in which electronnuclear Coulomb attraction is replaced by harmonic confinement. Furthermore, the interfermion interaction u(r12) between electrons at separation r12 is taken to be of inverse square form GPCH_A_445891_O_XML_IMAGES\GPCH_A_445891_O_ILM0001.gif With these model simplifications, it then proves possible to obtain an exact analytical expression for the groundstate energy density functional. Turning to current usage of density functional theory of inhomogeneous Fermion liquids, in terms of a onebody potential V(r), the singleparticle (s) kinetic energy functional Ts[n] is next considered, for the experimentally interesting case of ultracold Fermion vapours which are magnetically trapped. This is again the case of harmonic confinement. Results for Ts[n] for different dimensionalities have been obtained analytically for such systems and are summarized. The intimate relationship between this kinetic energy Ts and the exchange energy Ex is then exhibited, the offdiagonal density, or idempotent Dirac density matrix now being invoked. In turn this latter quantity can be related to the groundstate density n(r) via a partial differential equation. Finally, some brief discussion is given of the, as yet unsolved, problem of the electronelectron correlation energy.   
Language 



English
 
Source (journal) 



Physics and chemistry of liquids.  London  
Publication 



London : 2010
 
ISSN 



00319104
 
Volume/pages 



48:2(2010), p. 141155
 
ISI 



000277647300001
 
Full text (Publisher's DOI) 


  
