The functional renormalization group for zero-dimensional quantum systems in and out of equilibrium

Aachen / Publikationsserver der RWTH Aachen University (2010) [Dissertation / PhD Thesis]

Page(s): 219 S. : Ill., graph. Darst.


We study transport properties of quantum impurity systems using the functional renormalization group. The latter is an RG-based diagrammatic tool to treat Coulomb interactions in a fast and flexible way. Prior applications, which employed a simple first-order (Hartree-Fock-like) scheme to truncate the FRG flow equations within the Matsubara formalism, succeeded in accurately describing linear transport of various quantum dot geometries at zero temperature T=0. In a nutshell, advance in this Thesis is three-fold. First, we introduce a frequency-dependent second-order approximation in order to eventually compute finite-energy properties such as the conductance at T>0 (mainly focusing on the single impurity Anderson model). Second, a generalisation of the Hartree-Fock-like approach to Keldysh space allows for addressing the non-equilibrium steady-state dynamics of the interacting resonant level model. Third, we investigate the physics of a quantum dot Josephson junction as well as the charging of a single narrow level using the first-order scheme.



Karrasch, Christoph


Meden, Volker


  • URN: urn:nbn:de:hbz:82-opus-33468