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We present the results of theoretical investigation on some of the ground-state properties and dynamical behavior of two-dimensional systems. A great variety of low-dimensional systems has recently become available for experiment due to advances in semiconductor technology. However, many basic questions concerning the behavior of charge carriers in systems of low dimensionality are not yet fully understood. We address some of these open questions. Firstly, we calculate the magnetoconductivity of a quantum wire formed from a two-dimensional electron gas by additional lateral confinement in a parabolic potential. We consider two mechanisms--scattering of electrons by acoustic phonons, and electron scattering by impurities accompanied by phonon emission or absorption. The conductivity is calculated through a distribution function, which is found by solving the Boltzmann kinetic equation in linear approximation upon the electric field. We demonstrate that the functional dependence of the conductivity due to phonon scattering remains the same as in the conventional three-dimensional case, but is weakened due to the quasi-one-dimensional nature of the problem. We also show that the temperature -dependent part of the conductivity is dominated by phonon -assisted impurity scattering, and is, therefore, affected by the interference of different scattering mechanisms. Secondly, we study the long-range order (both translational and orientational) in the ground state of a coupled double-layer electron hole system. To qualitatively describe the disorder and topological defects in the system, we calculate the radial and angular correlation functions in the case of the finite system with equal electron and hole densities, for different densities of electrons and holes, and for a system with a jump in the interlayer separation. We also discuss defect formation and interaction with the strain field. Finally, we analytically calculate the dielectric function in a strongly coupled double-layer electron hole system with equal densities of the carriers. By obtaining the analytical expressions for both real and imaginary parts of the dielectric function, we find the asymptotic behavior of the screened interparticle potential at long distances at low temperatures. The imaginary part of the inverse dielectric function allows us to determine possible collective excitations in a system of interacting polarized dipoles.

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