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This lecture notes is about the role of electron-electron interactions in low dimensional systems and its transport properties.
It begins with a review of the pair-distribution function theory of electron liquid systems taking into account the electron-electron interactions. We extend the theory for highly correlated system such two- and one-dimensional electron liquids. We then
review the microscopic theory of the local-field factors and calculate the quasiparticle properties in two-dimension electron liquid and compare our results with those measured by recent
experiments. The physics of two-dimension bilayer structures are revised and are immediately applied to the study of charged Coulomb drag effects in a bilayer electron-electron system and results are compared with experimental data. As a final application, the Luttinger theory is discussed and we compare our recent calculations with those obtained from quantum Monte Carlo simulation for one dimensional electron liquid.
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