Show description

The experimental values were taken from Knight et al. (1985). PPJM indicates the approximation with pseudo-potential of Bachelet et al. (1982), PHJM indicates the approximation with the pseudo-Hamiltonian of Bachelet et al. (1989). As can be seen from the table, the pseudo-potential and pseudo-Hamiltonian models, when compared to jellium model (JM), much reduce the discrepancy between experimental and LDA results. Quantum dots Recently, nanotechnologies (1 nanometre = 1 0 - 9 metres) based on semiconductor heterostructures (for example, GaAs/Ga x Alj_ x As) allowed the realization of quantum wires and dots: these are specific objects to study the physics of low-dimensionality electrons.

128) is a condition which is imposed on /k,k' by translational invariance. 121). 130) enable for the determination of the Landau parameter F(. In order to establish a connection between F£ and a measurable quantity, let us assume that the hydrodynamic regime holds, and let us look for Euler-like equations for the density variations. 131) m —' oe k m kk' where we have used the result ^ k kjl(5n(k, r, t))coil = 0, which results from the current being conserved during collisions. However, the fact that the collision term does not change the quasiparticle density and their current, does not mean that it is not relevant in the hydrodynamic regimes where WT -C 1.

4) be stationary with respect to variations of (2-5) we obtain the Hartree-Fock equations: V2 2m + «ext(r)) ^ ( r , ") + E / dr'V*(r', (r - r') x [ ^ ( r , c 7 ) ^ ( r ' , o - ' ) - ^ ( r ' , c T ' ) ^ ( r , o - ) ] =enpi(r,a). 8) and cr||u' means that the spins must be parallel, since otherwise the exchange term vanishes. e. 9)] is non-local. In the Hartree theory only the local (direct) term U(r) is considered. The HF equations form a system of TV coupled integral-differential equations.