Correlation effects in quantum dots and wires

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In this project we investigate correlation effects in (quasi) one-dimensional quantum wires and in “zero”-dimensional quantum dots with a particular focus on the transport properties of such systems in the linear response regime and singleparticle spectral properties. We have successfully applied a truncation scheme leading to a static self-energy to problems of direct experimental relevance (“phase lapse puzzle” and charging of multi-level dots, Josephson current through correlated quantum dot). The static approximation can only be used in situation in which inelastic processes are irrelevant (e.g. temperatur T = 0 conductance). We thus extended the truncation scheme and kept the frequency dependence of the two-particle vertex which within the one-particle irreducible functional RG leads to a frequency dependent self-energy. We applied this scheme to study the singleimpurity Anderson model (in the appropriate parameter regime dominated by spin fluctuations) and the interacting resonant level model (dominated by charge fluctuations). We discussed the merits and drawbacks of this scheme. We will try to improve on the latter (higher-order corrections). Next we will use the frequency dependent approximation to investigate more complex systems of quantum dots showing a physics which is dominated by the interplay of the Kondo effect and other interactions (such as the RKKY). We will extend the frequency dependent scheme to study quantum wires. An interesting question is the crossover between bulk and boundary Luttinger liquid physics. Finally, we will use the frequency dependent scheme to study fermionic systems coupled to bosons (e.g. local electronic levels coupled to phonons.)