2012/09/30 by Christine C. Dantas · 1 citation
Physics and Astronomy · #Noncommutative and Quantum Gravity Theories #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics #gr-qc
paper · pdf · doi:10.1007/s10701-012-9692-2
published as Foundations of Physics, Volume 43, Issue 2, pp 236-242, 2013 · 6 pages, accepted for publication in Foundations of Physics; minor changes in accordance with referee's suggestion
arxiv created 2012/11/16 · openalex publication_date 2012/12/05 · arxiv updated 2013/01/25 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/29
The quantum evolution equation of Loop Quantum Cosmology (LQC) -- the quantum Hamiltonian constraint -- is a difference equation. We relate the LQC constraint equation in vacuum Bianchi I separable (locally rotationally symmetric) models with an integrable differential-difference nonlinear Schrödinger type equation, which in turn is known to be associated with integrable, discrete Heisenberg spin chain models in condensed matter physics. We illustrate the similarity between both systems with a simple constraint in the linear regime.