Towards the fractional quantum Hall effect: a noncommutative geometry perspective

zbMath1105.81068arXivcond-mat/0502356MaRDI QIDQ5488012

Varghese Mathai, Matilde Marcolli

Publication date: 13 September 2006

Full work available at URL: https://arxiv.org/abs/cond-mat/0502356

zbMATH Keywords

electronsPontryagin dualityHall conductanceblock theoryBrillouin zonesHarper operators

Mathematics Subject Classification ID

Many-body theory; quantum Hall effect (81V70) Statistical mechanics of solids (82D20) Noncommutative geometry in quantum theory (81R60) Electromagnetic theory (general) (78A25) Noncommutative geometry (à la Connes) (58B34)

Related Items (13)

Spectral decimation of a self-similar version of almost Mathieu-type operators ⋮ Quantum Hall Effect and Noncommutative Geometry ⋮ Anyons in geometric models of matter ⋮ The geometry of the double gyroid wire network: quantum and classical ⋮ Fractional quantum numbers via complex orbifolds ⋮ On the Lyapunov theory for functional differential equations of fractional order ⋮ On twisted Fourier analysis and convergence of Fourier series on discrete groups ⋮ Lieb-Schultz-Mattis theorem and the filling constraint ⋮ Singular Geometry of the Momentum Space: From wire networks to quivers and monopoles ⋮ Applications of noncommutative geometry in function theory and mathematical physics ⋮ Theoretical Properties of Materials Formed as Wire Network Graphs from Triply Periodic CMC Surfaces, Especially the Gyroid ⋮ Spectral actions for q-particles and their asymptotics ⋮ Fractional quantum numbers, complex orbifolds and noncommutative geometry

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