What question did this study set out to answer?

To determine whether a quantum state transported adiabatically along a closed parameter circuit acquires a path-dependent geometric phase factor in addition to the standard dynamical phase.

March 8, 1984Proceedings of the Royal Society of London A Mathematical and Physical Sciences

Quantal phase factors accompanying adiabatic changes

View Full Paper

Ask AI

Bookmark

Authors

MBMichael BerryUniversity of North Carolina at Chapel Hill

Discussion

Member takes

Implication

Theoretical analysis reveals anholonomic geometric phase shifts in adiabatically cycled quantum systems, indicating a universal topological origin for phenomena like the Aharonov-Bohm effect.

Key Points

To determine whether a quantum state transported adiabatically along a closed parameter circuit acquires a path-dependent geometric phase factor in addition to the standard dynamical phase.
Derived an exact mathematical formulation for the geometric phase factor using the spectrum and eigenstates of the Hamiltonian over a surface enclosing the circuit.
Modeled cyclic adiabatic transport across Hamiltonian degeneracies and calculated phase shifts for spin systems subjected to slowly rotating magnetic fields.
Identified a universal, non-integrable geometric phase factor exp{iγ(C)} that depends solely on circuit topology rather than transit duration.
Demonstrated that the geometric phase applies generally to both bosons and fermions, reproducing spinor sign reversal as a special case.
Established that the Aharonov-Bohm effect is fundamentally interpretable as an adiabatic geometric phase factor.

Cite This Study

Michael Berry (1984) studied this question.

synapsesocial.com/papers/696f155a50a360e9ca1198f2 https://doi.org/10.1098/rspa.1984.0023

View Full Paper

Ask AI

Bookmark

Implication

Theoretical analysis reveals anholonomic geometric phase shifts in adiabatically cycled quantum systems, indicating a universal topological origin for phenomena like the Aharonov-Bohm effect.

Quantal phase factors accompanying adiabatic changes

Discussion

Member takes

Implication

Key Points

Cite This Study

Quantal phase factors accompanying adiabatic changes

Discussion

Member takes

Implication

Key Points

Cite This Study

Also Consider

Also Consider