Low dimensional systems

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Recent experimental advancements have enabled the testing of fundamental physical concepts related to electron motion in low dimensions. The ability to produce and control novel structures in the sub-micrometer range has become a reality, particularly in semiconductors, which confine electron motion in two-dimensional heterostructures. The quantum Hall effect emerged as a significant highlight of the new physics revealed by this confinement. Technological progress has led to the development of additional artificial devices, such as quasi one-dimensional quantum wires and quantum dots, which exhibit behaviors markedly different from three- and two-dimensional systems, especially regarding electron transport and light interaction. Despite rapid advancements in technology and experimental techniques, our theoretical understanding of phenomena like the quantum Hall effect remains rudimentary. In low-dimensional structures, the interactions between electrons and other factors, such as lattice vibrations or light, give rise to new phenomena that differ significantly from those observed in bulk materials. While the theoretical framework for electronic transport properties in small devices is relatively well-established, it often neglects the complexities introduced by these interaction processes.