2014/02/26 by Murray T. Batchelor · 1 citation
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Cold Atom Physics and Bose-Einstein Condensates #Domain (mathematical analysis) #Field (mathematics) #Integrable system #Matrix (chemical analysis) #Object (grammar) #Open quantum system #Product (mathematics) #Quantum #Quantum many-body systems #Scattering #cond-mat.quant-gas #math-ph #math.MP
paper · pdf · doi:10.1142/s0217979214300102
published as Int. J. Mod. Phys. B 28 (2014) 1430010 · 13 pages, 8 figures. Based on Invited Talk, Conference in Honour of the 90th Birthday of Freeman Dyson, Singapore, Aug 26-29, 2013
arxiv created 2014/02/26 · openalex publication_date 2014/04/01 · arxiv updated 2014/06/06 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
The scattering matrix (S-matrix), relating the initial and final states of a physical system undergoing a scattering process, is a fundamental object in quantum mechanics and quantum field theory. The study of factorized S-matrices, in which many-body scattering factorizes into a product of two-body terms to yield an integrable model, has long been considered the domain of mathematical physics. Many beautiful results have been obtained over several decades for integrable models of this kind, with far reaching implications in both mathematics and theoretical physics. The viewpoint that these were only toy models changed dramatically with brilliant experimental advances in realizing low-dimensional quantum many-body systems in the lab. These recent experiments involve both the traditional setting of condensed matter physics and the trapping and cooling of atoms in optical lattices to engineer and study quasi-one-dimensional systems. In some cases the quantum physics of one-dimensional systems is arguably more interesting than their three-dimensional counterparts, because the effect of interactions is more pronounced when atoms are confined to one dimension. This article provides a brief overview of these ongoing developments, which highlight the fundamental importance of integrability.