Abstract
A quantal system in an eigenstate, slowly transported round a circuit C by varying parameters R in its Hamiltonian Ĥ(R), will acquire a geometrical phase factor exp{iγ(C)} in addition to the familiar dynamical phase factor. An explicit general formula for γ(C) is derived in terms of the spectrum and eigenstates of Ĥ(R) over a surface spanning C. If C lies near a degeneracy of Ĥ, γ(C) takes a simple form which includes as a special case the sign change of eigenfunctions of real symmetric matrices round a degeneracy. As an illustration γ(C) is calculated for spinning particles in slowly-changing magnetic fields; although the sign reversal of spinors on rotation is a special case, the effect is predicted to occur for bosons as well as fermions, and a method for observing it is proposed. It is shown that the Aharonov-Bohm effect can be interpreted as a geometrical phase factor.
Keywords
EigenfunctionPhysicsEigenvalues and eigenvectorsBosonHamiltonian (control theory)Degeneracy (biology)Geometric phaseFermionAdiabatic processSpinorSign (mathematics)Quantum mechanicsPhase (matter)Mathematical physicsMathematicsMathematical analysis
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Publication Info
- Year
- 1984
- Type
- article
- Volume
- 392
- Issue
- 1802
- Pages
- 45-57
- Citations
- 8761
- Access
- Closed
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Cite This
Michael Berry
(1984).
Quantal phase factors accompanying adiabatic changes.
Proceedings of the Royal Society of London A Mathematical and Physical Sciences
, 392
(1802)
, 45-57.
https://doi.org/10.1098/rspa.1984.0023
Identifiers
- DOI
- 10.1098/rspa.1984.0023