Berlin 2015 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 15: Statistical Physics - general

DY 15.2: Talk

Tuesday, March 17, 2015, 09:45–10:00, BH-N 334

Canonical approach to equilibrium properties of interacting quantum gases — Quirin Hummel, Juan Diego Urbina, and •Klaus Richter — Institut für Theoretische Physik, Universität Regensburg, 93040 Regensburg, Germany

It is generally accepted that the equilibrium properties of quantum gases give the same results for the canonical and grand canonical ensemble. For finite systems well below the thermodynamic limit, however, this equivalence breaks down. The total number of particles cannot be fixed within the grand canonical formalism where this quantity is subject to thermal and quantum fluctuations. This poses a serious problem, as most of the powerful techniques to deal with quantum and interaction effects in quantum gases are based on the grand canonical formalism.

In this contribution we present a purely canonical approach, with the specific intention to obtain virial-type expansions for finite systems of interacting identical particles, including the equation of state and (local and non-local) pair correlations. In our formalism the canonical partition function is given by a finite expansion in the inverse temperature, thus providing a closed explicit form for the quantum equation of state. We also discuss the thermodynamic limit and the effect of interactions and particle symmetry on the many-body spectra.