In this thesis mesoscopic structures intermediate in size between classical macroscopic objects and quantum mechanical objects as atoms are treated. The size of mesoscopic systems are of the same order as the wavelength of the electrons, which makes it necessary to take quantum mechanics into account. However the systems are much larger than atoms and molecules and provide a link between classical and quantum physics. These systems are very interesting both for understanding fundamental physics and technologically, since semiconductor components in about a decade will be small enough to make quantum mechanical effects important.

The mesoscopic systems, or nanostructures as they are also called due to their size of about 10 - 1000 nm (nanometer), are fabricated from GaAs/ A1GaAs heterostructures. The A1GaAs is n-doped in order to create a two-dimensional electrongas (2DEG) between the GaAs and A1GaAs. Further constriction in the movement of the electrons are made by applying a gate voltage to the gate at the top of the heterostructure.

Several different kinds of models for have been used to investigate different aspects of mesoscopic systems. The models are ranging from a basically onedimensional model calculating the conductance over a quantum point contact with an assumed linear potential drop to a realistic model for calculating the conductance through an arbitrary mesoscopic system knowing the gate structure and the physical structure of the heterostructure. In the latter model the potential in the 2DEG is calculated using a self-consistent Thomas-Fermi method and a hybrid recursive Green's function method uses this potential to yield the conductance.

Other investigations made in this thesis are electron transport in quantum dots coupled in a deterministic aperiodic order and studies of chaos in mesoscopic systems. One interesting aspect of studying chaos in mesoscopic systems is that classical and quantum mechanical measures of chaos can be studied for the same system, which have been done here for several different smooth potentials. The weak localization peak for the conductance at low magnetic field has been suggested to be related to the underlying classical dynamics and here this is investigated and partially questioned. A recently suggested nearest neighbor energy level distribution for mixed regular and chaotic system, called semi-Poisson distribution, intermediate between the Poisson (regular) and Wigner ( chaotic) distributions have been found in fundamentally different systems. These systems are for a quantum dot with soft potential and in a quantum dot with spin-orbit coupling.