Noncommutative quantum Hall effect and Aharonov–Bohm effect
نویسندگان
چکیده
منابع مشابه
Quantum Hall Effect and Noncommutative Geometry
Abstract. We study magnetic Schrödinger operators with random or almost periodic electric potentials on the hyperbolic plane, motivated by the quantum Hall effect (QHE) in which the hyperbolic geometry provides an effective Hamiltonian. In addition we add some refinements to earlier results. We derive an analogue of the Connes-Kubo formula for the Hall conductance via the quantum adiabatic theo...
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In this paper we give a survey of some models of the integer and fractional quantum Hall effect based on noncommutative geometry. We begin by recalling some classical geometry of electrons in solids and the passage to noncommutative geometry produced by the presence of a magnetic field. We recall how one can obtain this way a single electron model of the integer quantum Hall effect. While in th...
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For the lowest Landau level, noncommutative quantum mechanics and the Landau Hamiltonian are equivalent theories. Using this fact, we find that the parameter that measures the noncommutative effects is given by θ = 4h̄ c eH0 . From this formula we can infer a numerical estimate for θ using the data for the magnetic field used in the quantum Hall effect (H0 ∼ 12T ) and we getting that the θ = 0.6...
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ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and Theoretical
سال: 2007
ISSN: 1751-8113,1751-8121
DOI: 10.1088/1751-8113/40/33/024