Density-functional Theory Of Long-range Interaction In One-dimensional Fermi Gas

With the development of nanotechnology, we can successfully prepare a pure one-dimensional quantum gas in experiment,for example, semiconductor quan-tum wires,single-well carbon nanotubes.One-dimensional fermi gas systems are interested by many theoretical and experimental researchers.We know the differ-ent between the one-dimensional electron gas and ideal Fermi iquid.Due to the im-portant role played by the electronic-electronic interaction in one-dimensional;it is fail to describe such a system by traditional Landau theory.There have been many studies on ground state characteristics,spin correlation effects and spin-charge separation in one-dimensional electron gas.Different from short-range interac-tion,the long-range interaction in one-dimensional fermi gas is of better practical significance,and is attracting more interest.This paper mainly study spin polarized long-range interacting Fermi gases in one-dimensional with density functional theory. This research provide can be used for the one-dimensional Wigner crystallization.In the first chapter we introduce the background about quasi one-dimensional system and density functional theory.In the second chapter,we give the theory model of one-dimensional electron gas,illustrate the conditions being quasi one-dimensional electronic gas:rs》(?).At the same time we calculate the two-body hard-core model and the char-acteristics of δ potential.Second, we deduce the effective potential and Hamil-tonian of one-dimensional electron gas.Then,we discuss the exchange-correlation energy and exchange-correlation potential with the lattice diffusion Monte carlo method(LRDMC) provided by Michele Casula.Finally,we discuss the ground state properties of one-dimensional electronic gas.If only consider even electronic num-ber,the peaks of the density distribution is N/2.In the third chapter, we use the spin density-functional theory to solve the ground state of spin polarized long-range interaction in one-dimensional elec-tronic system.We build spin polarization exchange-correlation potential. According to the parametric formula of spin polarization exchange-correlation energy by Shulenburger,we discuss the relationship between spin polarization exchange-correlation energy and spin and density. Then we give the detailed exchange-correlation potential.Conclusion and outlook are given in the chapter four.