1999/10/25 by Ali Mostafazadeh · 6 citations
Mathematics · Physics and Astronomy · #Adiabatic process #Classical mechanics #Cold Atom Physics and Bose-Einstein Condensates #Geometric phase #Hamiltonian (control theory) #Mathematical optimization #Mathematics #Particle in a box #Perturbation (astronomy) #Perturbation theory (quantum mechanics) #Physics #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Quantum mechanics #Rayleigh scattering #Statistical physics #hep-th #quant-ph
paper · pdf · doi:10.1088/0305-4470/32/47/311
published in Journal of Physics A Mathematical and General 32(47), 8325-8340 (Institute of Physics) · Plain Latex, accepted for publication in J. Phys. A: Math. Gen
arxiv created 1999/10/25 · openalex publication_date 1999/11/11 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We use the Rayleigh-Schrödinger perturbation theory to calculate the corrections to the adiabatic geometric phase due to a perturbation of the Hamiltonian. We show that these corrections are at least of second order in the perturbation parameter. As an application of our general results we address the problem of the adiabatic geometric phase for a one-dimensional particle which is confined to an infinite square well with moving walls.