Newtonian Adiabatics Unified
Abstract
Description
Newtonian adiabatics is the consistent truncation of the adiabatic approximation to second order in small velocities. To be complete it must unify two hitherto disjoint intellectual streams in the study of adiabatic motion. The newer stream focuses on Berry's induced vector potential, or geometric magnetism, and Provost and Vallee's induced scalar potential, reflecting geometry in Hilbert space. The older stream focuses on Inglis' induced inertia, influencing the geometry of adiabatic-parameter space. Starting with the Hamiltonian of the newer stream, unification is simple: A naive or primitive inertia, whose inverse appears in two terms of that Hamiltonian, is replaced by the convention-independent sum of primitive and induced inertia tensors.
6 pages. New footnote on essential fourth-order term in velocity for Darwin Lagrangian, plus cleanup of unclear points, plus added references. To appear in Phys. Rev. A
6 pages. New footnote on essential fourth-order term in velocity for Darwin Lagrangian, plus cleanup of unclear points, plus added references. To appear in Phys. Rev. A