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Landau problem, magnetic translations and noncommutative tori

Todor Popov
Institution: 
INRNE, Sofia
Location: 
A-134
Schedule: 
Friday, February 17, 2017 - 10:00
Abstract: 

We revise the Landau problem of an electron in a constant magnetic field. The free Hamiltonian is invariant with respect to the Zak's magnetic translations. Under the assumption of periodicity the magnetic translations  generate  a non-commutative quantum torus. For rational values of the magnetic flux duality manifests as a Morita equivalence between finite modules of the non-commutative torus. Taking the spin of the electron into account we are naturally lead to a supersymmetric extension of the magnetic translations

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