Abstract
This thesis is composed of two parts. In part I, we investigate the 0.7 anomaly in the quantum point contact system. The origin of 0.7 G0 may be due to the Rashba spin-orbit interaction. A spatial uniform spin-orbit interaction together with Coulomb interaction will open a spin gap, while a non-uniform spin-orbit interaction may lead to a moment formation. We have both semiclassical and quantum mechanical approaches. In part II, we introduce a fluctuating bond model for cuprate high-temperature superconductivity, which provides a unified framework for both pseudogap and superconducting gap. This model captures the essence of cuprate conductivity and leads to a reasonable phase diagram with the help of ab initio simulation.