Project 4: Interacting Brownian motions and many-body systems

Participants

Stefan Adams, Jürgen Gärtner, Wolfgang König, Manfred Salmhofer

Summary

We investigate the low--temperature behaviour of dilute quantum many--particle models. Our main interest is in understanding the dependence of the free energy density and correlation functions in the Gross--Pitaevskii limit, as well as generalizations of this limits which correspond to slightly larger densities. We consider both the canonical and the grand canonical ensemble. 

The former is studied via the interacting Brownian motion representation, using large deviations techniques, the latter via coherent--state functional integrals, using techniques from constructive  quantum field theory. We also aim to investigate the connections between these two approaches.

Some related earlier preprints

  • Stefan Adams, Jean-Bernard Bru and Wolfgang König:
    • Large deviations for trapped interacting Brownian particles and paths
    The Annals of Probability 34:4, 1370-1422 (2006),
    Preprint, ps, Preprint, pdf

    Achievements of the Research Group

  • Stefan Adams, Jean-Bernard Bru and Wolfgang König:
    • Large systems of path-repellent Brownian motions in a trap at positive temperature
    Electronic Journal of Probability, Vol 11 (2006), paper No. 18, pages 460-485.

  • Stefan Adams, Wolfgang König:
    • Large deviations for many Brownian bridges with symmetrised initial-terminal condition
    Probab. Theory Relat. Fields 142, 79-124 (2008).
    published online

  • Stefan Adams, Tony Dorlas:
    • Asymptotic Feynman-Kac formulae for large symmetrised systems of random walks
    to appear in Annales de l'Institut Henri Poincaré (B) Prob. Stat.,
    Preprint.

  • Stefan Adams:
    • Large deviations for empirical path measures in cycles of integer partitions
    Preprint.

  • Stefan Adams, Tony Dorlas:
    • C^*-algebraic approach to the Bose-Hubbard model
    Jour. Math. Phys. 48, 103304-(1-14) (2007).
    Preprint.

  • Walter Pedra, Manfred Salmhofer:
    • Determinant bounds and the Matsubara UV problem of many-fermion systems
    Comm. Math. Phys., to appear (2008).
    DOI 10.1007/s00220-008-0463-z