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.
Quantum mechanics of periodic potentials, Bloch states
Berry phase corrections to semiclassical equations of motion
Semiclassical motion in applied fields
Semiclassical level quantization, the Maslov index as a geometric
phase
Anomalous Hall effect as a topological Fermi liquid property
--
[1] Bohm et al.,The geometric phase in quantum systems,
Springer, Berlin (2003), chapter 2.1-2.3.
[2] N.W. Ashcroft and N.D. Mermin, Solid State
Physics, chapters 12 and 13
[3] A. Bohm et al.,The geometric phase in
quantum systems, Springer, Berlin (2003),
chapter 12.1- 12.5
[4] G. Sundaram and Q. Niu, Phys. Rev. B 59, 14915 (1999).
[5] M. Berry, Annals of the New York Academy of
Science 755, 303 (1995).
[6] F.D.M. Haldane, Phys. Rev. Lett. 93, 206602 (2004).
[7] Z. Fang et al., The anomalous Hall effect and
Magnetic monopoles in momentum space,
Science 302, 92 (2003).
|