2016/08/31 by N. L. Harshman
Computer Science · Mathematics · Physics and Astronomy · #Adiabatic process #Classical mechanics #Cold Atom Physics and Bose-Einstein Condensates #Dimension (graph theory) #Geometry #Hamiltonian (control theory) #Homogeneous space #Limiting #Mathematics #Physics #Pure mathematics #Quantum Information and Cryptography #Quantum mechanics #Quantum tunnelling #Quantum, superfluid, helium dynamics #Statistical physics #Symmetry (geometry) #Theoretical physics #cond-mat.quant-gas #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1103/physreva.95.053616
published as Phys. Rev. A 95, 053616 (2017) · 17 pages in two-column format, 9+ figures; v2 heavily revised (especially introduction) and new references
openalex created_date 2016/09/16 · arxiv created 2017/04/06 · openalex publication_date 2017/05/16 · arxiv updated 2017/05/18 · openalex updated_date 2026/08/05
This article investigates the properties of a few interacting particles trapped in a few wells and how these properties change under adiabatic tuning of interaction strength and interwell tunneling. While some system properties are dependent on the specific shapes of the traps and the interactions, this article applies symmetry analysis to identify generic features in the spectrum of stationary states of few-particle, few-well systems. Extended attention is given to a simple but flexible three-parameter model of two particles in two wells in one dimension. A key insight is that two limiting cases, hard-core repulsion and no interwell tunneling, can both be treated as emergent symmetries of the few-particle Hamiltonian. These symmetries are the mathematical consequences of infinite barriers in configuration space. They are necessary to explain the pattern of degeneracies in the energy spectrum, to understand how degeneracies are broken for models away from limiting cases, and to explain separability and integrability. These symmetry methods are extendable to more complicated models and the results have practical consequences for stable state control in few-particle, few-well systems with ultracold atoms in optical traps.