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      Many-body properties of one-dimensional systems with contact interaction

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      Author
      Demirel, Ekrem
      Advisor
      Tanatar, Bilal
      Date
      1999
      Publisher
      Bilkent University
      Language
      English
      Type
      Thesis
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      Abstract
      The one-dimensional electron systems are attracting a lot of interest because of theoretical and technological implications. These systems are usually fabricated on two-dimensional electron systems by confining the electrons in one of the remaining free directions by using nanolithographic techniques. There are also naturally occuring orgnanic conductors such as TTF-TCNQ whose conductivity is thought to be largely one-dimensional. The one-dimensional electron systems are important theoretically since they constitute one of the simplest many-body systems of interacting fermions with properties very different from three- and two-dimensional systems. The one-dimensional electron gas with a repulsive contact interaction model can be a useful paradigm to investigate these peculiar many-body properties. The system of bosons are also very interesting because of the macroscopic effects such as Bose-Einstein condensation and superfluidity. Another motivation to study one-dimensional Bose gas is the theoretical thought that one-dimensional electron gas gives boson gas characteristics. This work is based on the study of correlation effects in one-dimensional electron and boson gases with repulsive contact interactions. The correlation effects are described by a localfield correction which takes into account the short-range correlations. We use Vashishta-Singwi approach to calculate static correlation effects in onedimensional electron and boson gases. We find that Vashishta-Singwi approach gives better results than the other approximations. We also study the dynamical correlation effects in a one-dimensional electron gas with contact interaction within the quantum version of the self-consistent scheme of Singwi et al. (STLS) We calculate frequency dependent local-field corrections for both density and spin fluctuations. We investigate the structure factors, spin-dependent pair-correlation functions, and collective excitations. We compare our results with other theoretical approaches.
      Keywords
      One-dimensional electron gas
      Bose gas
      contact interaction
      correlation effects
      local-field correction
      STLS approximation
      Vashishta-Singwi approximation
      structure factors
      paircorrelation functions
      collective excitations
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      http://hdl.handle.net/11693/18120
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      • Dept. of Physics - Master's degree 160
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