A variational formula for the free energy of a many-Boson system

  • Wolfgang König (Universität Leipzig)
Raum 01/22 Universität Leipzig (Leipzig)


We consider $N$ Bosons in a box with volume $N/\rho$ under the presence of a mutually repellent pair potential. Denote by $H_N$ the corresponding Hamilton operator with either zero or periodic boundary condition. The symmetrised trace of $e^{-\beta H_N}$ describes the Bosons at positive temperature $1/\beta$. Our main result is a variational formula for the limiting free energy, for any fixed values of the particle density $\rho$ and the inverse temperature $\beta$, in any dimension. The main tools are a description in terms of a marked Poisson point process and a large-deviation analysis of the stationary empirical field. The resulting variational formula in particular describes the asymptotic cycle structure that is induced by the symmetrisation in the Feynman-Kac formula. We close with a short discussion of the relation to Bose-Einstein condensation.

(joint work in progress with S. Adams and A. Collevecchio)

20.11.06 26.01.09

Oberseminar Statistical Mechanics

Universität Leipzig Felix-Klein-Hörsaal

Katharina Matschke

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