Three-body scattering from nonperturbative flow equations

Details Three-body scattering from nonperturbative flow equations Three-body scattering from nonperturbative flow equations

2007-12-18

arxiv.org/abs/0712.2846v2

Phys.Rev.C78:034001,2008

Physics

Condensed Matter

Statistical Mechanics

13 pages, 4 figures, references added, discussion improved

Scientific paper

10.1103/PhysRevC.78.034001

We consider fermion-dimer scattering in the presence of a large positive scattering length in the frame of functional renormalization group equations. A flow equation for the momentum dependent fermion-dimer scattering amplitude is derived from first principles in a systematic vertex expansion of the exact flow equation for the effective action. The resummation obtained from the nonperturbative flow is shown to be equivalent to the one performed by the integral equation by Skorniakov and Ter-Martirosian (STM). The flow equation approach allows to integrate out fermions and bosons simultaneously, in line with the fact that the bosons are not fundamental but build up gradually as fluctuation induced bound states of fermions. In particular, the STM result for atom-dimer scattering is obtained by choosing the relative cutoff scales of fermions and bosons such that the fermion fluctuations are integrated out already at the initial stage of the RG evolution.

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