Two-dimensional electron gas in a periodic potential and external magnetic field: states of pairs and three-particle systems
Abstract
The group-theoretical classification of states of identical particle pairs is presented. Then obtained states are coupled with those of an antiparticle to construct states of a three-particle system. Investigations are performed using products of irreducible projective representations of the 2D translation group. For a given BvK period N degeneracy of pair states is N, whereas three-particle states are N^2-fold degenerated. It has to be underlined that the case of even N is more complicated since pair states are labelled by four inequivalent irreducible projective representations. The problem of symmetry properties with respect to particles transposition is briefly discussed.
- Publication:
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arXiv e-prints
- Pub Date:
- December 2002
- DOI:
- 10.48550/arXiv.cond-mat/0212396
- arXiv:
- arXiv:cond-mat/0212396
- Bibcode:
- 2002cond.mat.12396F
- Keywords:
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- Condensed Matter - Mesoscopic Systems and Quantum Hall Effect
- E-Print:
- 8 pages, LaTeX 2e