A note on the Berry phase for systems having one degree of freedom
- 7 April 1988
- journal article
- editorial
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 21 (7), 1725-1727
- https://doi.org/10.1088/0305-4470/21/7/033
Abstract
A one-dimensional arbitrary system with quantum Hamiltonian H(q, p) is shown to acquire the 'geometric' phase gamma (C)=(1/2) contour integral c(Podqo-qodpo) under adiabatic transport q to q+q+qo(t) and p to p+po(t) along a closed circuit C in the parameter space (qo(t), po(t)). The non-vanishing nature of this phase, despite only one degree of freedom (q), is due ultimately to the underlying non-Abelian Weyl group. A physical realisation in which this Berry phase results in a line spread is briefly discussed.Keywords
This publication has 11 references indexed in Scilit:
- Molecular Kramers degeneracy and non-Abelian adiabatic phase factorsPhysical Review Letters, 1987
- Phase change during a cyclic quantum evolutionPhysical Review Letters, 1987
- Some geometrical considerations of Berry’s phasePhysical Review D, 1987
- Observation of Berry's Topological Phase by Use of an Optical FiberPhysical Review Letters, 1986
- Manifestations of Berry's Topological Phase for the PhotonPhysical Review Letters, 1986
- Angle variable holonomy in adiabatic excursion of an integrable HamiltonianJournal of Physics A: General Physics, 1985
- Classical adiabatic angles and quantal adiabatic phaseJournal of Physics A: General Physics, 1985
- Appearance of Gauge Structure in Simple Dynamical SystemsPhysical Review Letters, 1984
- Quantal phase factors accompanying adiabatic changesProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1984
- Holonomy, the Quantum Adiabatic Theorem, and Berry's PhasePhysical Review Letters, 1983