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In this dissertation we use sophisticated numerical methods in order toexamine ground-state (GS) properties of two types of quantum systems withelectron electron interactions: A quantum dot (QD) and a nano-wire. In thefirst half of the work we study a system of a single level coupled to aone-dimensional wire with interacting spinless electrons, when the wire iseither clean or disordered. We utilize the density-matrix renormalization-group(DMRG) method to investigate the influence of the level on severalthermodynamic properties of the clean interacting wire, which can be in one oftwo phases: Tomonaga-Luttinger liquid and charge density wave phases. When thewire is disordered, we investigate the Friedel oscillations, exploring thedifference between the two phases and comparing them to the cleannon-interacting case, for which we develop an exact formula for theoscillations. In the second half of the dissertation we study two cases of anisolated two-dimensional QD. We begin by an investigation of a new numericalmethod, the particle-hole DMRG (PH-DMRG), which is used to calculate the GSenergy of a disordered QD consisting of interacting spinless electrons. We showthat this method is much more accurate than the Hartree-Fock method, and wesuggest an improvement of the algorithm, which reduces the error rate by almost30 percents. Finally we study the magnetization of a QD with spin 1/2electrons, in the presence of spin-orbit coupling and interactions. Wecalculate the g-factor and the expectation values of the spin operators in theGS, and find that when the QD is occupied by an even number of electrons, theGS can have a finite magnetization.

Influence of spin and interactions on quantum dots and nano-wires