A Quantum point contact (QPC) is a one dimensional constriction, separating two extended electronudsystems allowing transport between them only though a short and narrow channel.udThe linear conductance of QPCs is quantized in units of the conductance quantumudG_Q=2e^2/h, where e is the electron charge and h is Planck's constant. Thus the udconductance shows a staircase when plotted as a function of gate-voltage whichuddefines the width of the channel. In addition measured curves show a shoulder-likeudstep around 0.7G_Q. In this regime QPCs show anomalous behaviour in quantitiesudlike electrical or thermal conductance, noise, and thermopower, as a function ofudexternal parameters such as temperature, magnetic field, or applied voltage. Theseudphenomena, collectively known as the 0.7-anomaly in QPCs are subject of controversialuddiscussion.ududThis thesis offers a detailed description of QPCs in the parameter regime of the ud0.7-anomaly. A model is presented which reproduces the phenomenology of the ud0.7-anomaly. We give an intuitive picture and a detailed description of the udmicroscopic mechanism leading to the anomalous behavior. Further, we offer detailedudpredictions for the behavior of the 0.7-anomaly in the presence of spin-orbitudinteractions. ududOur best theoretical results were achieved using an approximation scheme within the udfunctional renormalization group (fRG) which we developed to treat inhomogeneousudinteracting fermi systems. This scheme, called the coupled ladder approximationud(CLA), allows the flow of the two-particle vertex to be incorporated even if the udnumber of interacting sites N, is large, by reducing the number of independentudvariables which represent the two-particle vertex from O(N^4) toudO (N^2).
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