Non Perturbative Renormalization Group and Bose-Einstein Condensation
| dc.creator | Blaizot, Jean-Paul | |
| dc.date | 2007-12-28 | |
| dc.date.accessioned | 2026-07-07T08:51:51Z | |
| dc.date.available | 2026-07-07T08:51:51Z | |
| dc.description | These lectures are centered around a specific problem, the effect of weak repulsive interactions on the transition temperature $T_c$ of a Bose gas. This problem provides indeed a beautiful illustration of many of the techniques which have been discussed at this school on effective theories and renormalization group. Effective theories are used first in order to obtain a simple hamiltonian describing the atomic interactions: because the typical atomic interaction potentials are short range, and the systems that we consider are dilute, these potentials can be replaced by a contact interaction whose strength is determined by the s-wave scattering length. Effective theories are used next in order to obtain a simple formula for the shift in $T_c$: one exploits there the fact that near $T_c$ the physics is dominated by low momentum modes whose dynamics is most economically described in terms of classical fields; the ingredients needed to calculate the shift of $T_c$ can be obtained from this classical field theory. Finally the renormalization group is used both to obtain a qualitative understanding, and also as a non perturbative tool to evaluate quantitatively the shift in $T_c$. | |
| dc.description | Lectures given at the 2006 ECT* School "Renormalization Group and Effective Field Theory Approaches to Many-Body Systems", Trento, Italy. Late submission to arXiv | |
| dc.identifier | https://arxiv.org/abs/0801.0009 | |
| dc.identifier | http://arxiv.org/abs/0801.0009 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/145082 | |
| dc.subject | Statistical Mechanics | |
| dc.title | Non Perturbative Renormalization Group and Bose-Einstein Condensation | |
| dc.type | text |