Application of the functional renormalization group to Bose systems with broken symmetry [Elektronische Ressource] / von Andreas Sinner

Application of the Functional Renormalization Groupto Bose systems with broken symmetryDissertationzur Erlangung des Doktorgradesder Naturwissenschaftenvorgelegt beim Fachbereich FB 13 Physikder Johann Wolfgang Goethe-Universit¨atin Frankfurt am MainvonAndreas Sinneraus KuibyschewFrankfurt (2009)(D 30)vom Fachbereich FB 13 Physik derJohann Wolfgang Goethe-Universit¨at als Dissertation angenommen.Dekan: Prof. Dr. Dirk-Hermann RischkeGutachter: Prof. Dr. Peter KopietzProf. Dr. Walter HoffstetterDatum der Disputation: 6. Juli 2009AbstractThe physics of interacting bosons in the phase with broken symmetry is determined bythe presence of the condensate and is very different from the physics in the symmetricphase. The Functional Renormalization Group (FRG) represents a powerful investiga-tion method which allows the description of symmetry breaking with high efficiency. Inthe present thesis we apply FRG for studying the physics of two different models in thebroken symmetry phase.In the first part of this thesis we consider the classical O(1)−model close to the criticalpoint ofthe second order phase transition. Employing atruncation scheme based ontherelevance of coupling parameters we study the behavior of the RG-flow which is shownto be influenced by competition between two characteristic lengths of the system. Wealso calculate the momentum dependent self-energy and study its dependence on bothlength scales.