The investigation of Hamiltonians that depend on slowly
(adiabatically) varying parameters lead to the discovery of
the Berry phase (geometric phase). The Berry phase has
found numerous applications in condensed matter physics.
Adiabatic approximation for time-dependent hamiltonians,
range of validity of this approximation,
Definition of Berry Phase and Mead-Berry vector potential.
Connection to differential one-forms, Gauge transformations,
Mead-Berry curvature.
Example, spinning quantum system in external magnetic field,
magnetic monopole potential.
Experiment, photonic Berry Phase in optical fibers.
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[1] Bohm et al.,The geometric phase in quantum systems,
Springer, Berlin (2003), chapter 2.1-2.3.
[2] M.V. Berry, Quantal phase factors accompanying
adiabatic changes, Proc. R. Soc. Lond. A 392,
45-57 (1984).
[3] A. Bohm et al.,The geometric phase in
quantum systems, Springer, Berlin (2003),
chapter 2.1-2.3,3.1-3.3.
[4] A. Tomita and R.Y. Chiao, Observation of Berry's
topological phase by use of an optical fiber,
Phys. Rev. Lett. 57, 937 (1986).
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