Heidelberg 2015 – scientific programme

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Q: Fachverband Quantenoptik und Photonik

Q 11: Quantum Gases: Fermions II

Q 11.4: Talk

Monday, March 23, 2015, 15:30–15:45, K/HS2

Canonical approach to equilibrium properties of interacting fermionic quantum gases — •Quirin Hummel, Juan Diego Urbina, and Klaus Richter — Institut für Theoretische Physik, Universität Regensburg, 93053 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 can not be fixed within the grand canonical formalism where by definition this quantity is always subject to thermal and quantum fluctuations except in the strict thermodynamic limit. This poses a serious problem, as most of the powerful techniques to deal with quantum and interaction effects in quantum gases depend in an essential way on the use of the grand canonical formalism. To the best of our knowledge, a purely canonical approach to address quantum and interaction effects on equilibrium thermodynamics of quantum gases with a fixed number of particles is not available.

In this contribution we present such an approach, with the specific intention to obtain virial-type expansions for finite fermionic systems, 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.