2012/02/29 by D. H. J. O’Dell, D. H. J. O'Dell · 1 citation
Mathematics · Physics and Astronomy · #Catastrophe theory #Classical mechanics #Cold Atom Physics and Bose-Einstein Condensates #Ergodic theory #Ergodicity #Fock space #Gravitational singularity #Hamiltonian (control theory) #Josephson effect #Mathematical analysis #Mathematical physics #Mathematics #Physics #Quantum #Quantum many-body systems #Quantum mechanics #Strong Light-Matter Interactions #Superconductivity #cond-mat.quant-gas
paper · pdf · doi:10.1103/physrevlett.109.150406
published as Phys. Rev. Lett. 109, 150406 (2012) · 5 pages, 3 figures. New references added plus a section on experimental realizability
arxiv created 2012/09/10 · openalex publication_date 2012/10/09 · arxiv updated 2012/10/17 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We study rainbow (fold) and cusp catastrophes that form in Fock space following a quench in a Bose Josephson junction. In the Gross-Pitaevskii mean-field theory, the rainbows are singular caustics, but in the second-quantized theory a Poisson resummation of the wave function shows that they are described by well-behaved Airy functions. The structural stability of these Fock space caustics against variations in the initial conditions and Hamiltonian evolution is guaranteed by catastrophe theory. We also show that the long-time dynamics are ergodic. Our results are relevant to the question posed by Berry [M. V. Berry, Nonlinearity 21, T19 (2008)]: Are there circumstances when it is necessary to second quantize wave theory in order to avoid singularities?