Symmetry and Natural Quantum Structures for Three-Particles in One-Dimension
arXiv:1607.00560 · doi:10.1142/9781786341419_0011
Abstract
How do symmetries induce natural and useful quantum structures? This question is investigated in the context of models of three interacting particles in one-dimension. Such models display a wide spectrum of possibilities for dynamical systems, from integrability to hard chaos. This article demonstrates that the related but distinct notions of integrability, separability, and solvability identify meaningful collective observables for Hamiltonians with sufficient symmetry. In turn, these observables induce tensor product structures on the Hilbert space that are especially useful for storing and processing quantum information and provide guidance to interpretation and phenomenology of quantum few-body physics.
This is an essay to be published as a book chapter in "Quantum Structural Studies: Classical Emergence from the Quantum Level", R.E. Kastner, J. Jeknic-Dugic, G. Jaroszkiewicz (Eds.), World Scientific. 24 pages preprint format