2004/10/18 by Patrick Dorey, Adam Millican-Slater, Roberto Tateo · 43 citations
Mathematics · Physics and Astronomy · #Angular momentum #Classical mechanics #Integrable system #Mathematical analysis #Mathematical physics #Mathematics #Neutrino Physics Research #Ode #Physics #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Quantum mechanics #Resummation #Schrödinger equation #Spontaneous symmetry breaking #Symmetry (geometry) #Symmetry breaking #WKB approximation #cond-mat.stat-mech #hep-th #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1088/0305-4470/38/6/010
published in Journal of Physics A Mathematical and General 38(6), 1305-1331 (Institute of Physics) · 29 pages, Latex, many figures. v2: sign typos fixed, and a reference added
arxiv created 2004/10/18 · openalex publication_date 2005/01/27 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
The mergings of energy levels associated with the breaking of symmetry in the model of Bender and Boettcher, and in its generalization to incorporate a centrifugal term, are analysed in detail. Even though conventional WKB techniques fail, it is shown how the ODE/IM correspondence can be used to obtain a systematic approximation scheme which captures all previously observed features. Nonperturbative effects turn out to play a crucial role, governing the behaviour of almost all levels once the symmetry-breaking transition has been passed. In addition, a novel treatment of the radial Schrödinger equation is used to recover the values of local and non-local conserved charges in the related integrable quantum field theories, without any need for resummation even when the angular momentum is nonzero.