2006/11/30 by André LeClair · 14 citations
Mathematics · Physics and Astronomy · #Ansatz #Bethe ansatz #Bose gas #Bose–Einstein condensate #Cold Atom Physics and Bose-Einstein Condensates #Condensed matter physics #Fermi Gamma-ray Space Telescope #Fermi gas #Formalism (music) #Integrable system #Mathematical physics #Physics #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Quantum electrodynamics #Quantum mechanics #Quasiperiodic function #Riemann hypothesis #cond-mat.stat-mech #hep-th #math-ph #math.MP #math.NT
paper · pdf · doi:10.1142/s0217751x08039451
published in International Journal of Modern Physics A 23(09), 1371-1391 (World Scientific) · version 3: additional appendix explains how the $ν$ to $1-ν$ duality of Riemann's $ζ(ν)$ follows from a special modular transformation in a massless relativistic theory
arxiv created 2007/09/18 · openalex publication_date 2008/04/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We apply the S-matrix based finite temperature formalism to nonrelativistic Bose and Fermi gases in 1+1 and 2+1 dimensions. For the (2+1)-dimensional case in the constant scattering length approximation, the free energy is given in terms of Roger's dilogarithm in a way analagous to the thermodynamic Bethe ansatz for the relativistic (1+1)-dimensional case. The 1d fermionic case with a quasiperiodic two-body potential is closely connected with the Riemann hypothesis.