2017/07/05 by K. Schönhammer · 1 citation
Chemistry · Mathematics · Physics and Astronomy · #Calculus (dental) #Canonical ensemble #Cold Atom Physics and Bose-Einstein Condensates #Grand canonical ensemble #Mathematical economics #Mathematics #Non canonical #Physics #Quantum, superfluid, helium dynamics #Spectroscopy and Laser Applications #Statistical physics #Statistics #cond-mat.stat-mech #quant-ph
paper · pdf · doi:10.1103/physreva.96.012102
published as Phys. Rev. A96, 012102 (2017) · Typo corrected in Eq.(58), one sentence added after Eq. (40)
openalex publication_date 2017/07/05 · arxiv created 2020/08/11 · arxiv updated 2020/08/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Wick's theorem for the expectation values of products of field operators for a system of noninteracting fermions or bosons plays an important role in the perturbative approach to the quantum many-body problem. A finite-temperature version holds in the framework of the grand canonical ensemble, but not for the canonical ensemble appropriate for systems with fixed particle number such as ultracold quantum gases in optical lattices. Here we present formulas for expectation values of products of field operators in the canonical ensemble using a method in the spirit of Gaudin's proof of Wick's theorem for the grand canonical case. The deviations from Wick's theorem are examined quantitatively for two simple models of noninteracting fermions.