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Hamiltonian theory of anyons in crystals. (English. Russian original) Zbl 1180.81065
J. Math. Sci., New York 151, No. 4, 3159-3166 (2008); translation from Fundam. Prikl. Mat. 12, No. 7, 129-139 (2006).
Summary: Semiclassical wave packets for electrons in crystals, subject to an external electromagnetic field, satisfy Hamiltonian equations. In \((2+1)\)-dimensions and in the limit of uniform fields, the symmetry group results in a two-folded Galilei algebra, incorporating an “exotic” central charge. It has the physical meaning of the Berry phase curvature. In the Hamiltonian scheme, we discuss possible deformations of this algebra and the physical meaning of what takes place.
81Q20 Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory
81Q70 Differential geometric methods, including holonomy, Berry and Hannay phases, Aharonov-Bohm effect, etc. in quantum theory
81V70 Many-body theory; quantum Hall effect
82D25 Statistical mechanical studies of crystals
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