2001/03/09 by Gerald V. Dunne, K. Rao, Kumar Rao · 1 citation
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Physics of Superconductivity and Magnetism #Quantum Chromodynamics and Particle Interactions #cond-mat #hep-ph #hep-th
paper · pdf · doi:10.1103/physrevd.64.025003
published as Phys.Rev. D64 (2001) 025003 · 17 pgs, 9 figs, RevTex4
arxiv created 2001/03/09 · openalex publication_date 2001/06/04 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We analyze the phemomenon of induced fermion number at finite temperature. At finite temperature, the induced fermion number <N> is a thermal expectation value, and we compute the finite temperature fluctuations, (ΔN)2=<N2>-<N>2. While the zero temperature induced fermion number is topological and is a sharp observable, the finite temperature induced fermion number is generically nontopological, and is not a sharp observable. The fluctuations are due to the mixing of states inherent in any finite temperature expectation value. We analyze in detail two different cases in 1+1 dimensional field theory: fermions in a kink background, and fermions in a chiral sigma model background. At zero temperature the induced fermion numbers for these two cases are very similar, but at finite temperature they are very different. The sigma model case is generic and the induced fermion number is nontopological, but the kink case is special and the fermion number is topological, even at finite temperature. There is a simple physical interpretation of all these results in terms of the spectrum of the fermions in the relevant background, and many of the results generalize to higher dimensional models.