This thesis deals with systems of interacting particles with very low energy in the limit where the particleparticle scattering is much larger than the range of the interactions. We use a quantumfieldtheory approach which allows us to study both fewbody and densematter systems in a unified framework. This allows to introduce composite fields of two and three particles (when appropriate). The quantum corrections are calculated nonperturbatively with the Functional RenormalisationGroup.We deal with three types of systems. First we study systems with three and four scalar particles. For threeparticle systems our framework describes the Efimov effect. During the FRG flow in the scaling limit, the fourparticle system has an infinite sequence of (unphysical) fourparticle states on top of each Efimov trimer. This is a case of super Efimov behaviour. Three of these fourparticle states survive to the physical limit. Two of these three states have been found in exact quantummechanical calculations, and have also been observed in gases of ultracold atoms.Next, this thesis studies systems of three and four spin1/2 particles. In the scaling limit, we find attractive fixed points for the three and fourparticle systems. Out of the scaling limit, we study atommolecule scattering and moleculemolecule scattering, in particular their scattering length. Finally, we study densematter systems of spin1/2 particles. This calculation includes all the two, three, and fourparticle interactions. These systems show spontaneous symmetry breaking: the twoparticle field has a finite classical value. We find the value of the atom gap in units of the chemical potential.
Date of Award  1 Aug 2015 

Original language  English 

Awarding Institution   The University of Manchester


Supervisor  Michael Birse (Supervisor) 

 Functional Renormalisation Group
 unitary Fermi gas
 tetramer
 ultracold atomic gases
Functional Renormalisation Group and Nuclear Matter
Jaramillo Avila, B. (Author). 1 Aug 2015
Student thesis: Phd