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تسجيل مستخدم جديدQuantum graphs and the integer quantum Hall effect
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We study the spectral properties of infinite rectangular quantum graphs in the presence of a magnetic field. We study how these properties are affected when three-dimensionality is considered, in particular, the chaological properties. We then establish the quantization of the Hall transverse conductivity for these systems. This quantization is obtained by relating the transverse conductivity to topological invariants. The different integer values of the Hall conductivity are explicitly computed for an anisotropic diffusion system which leads to fractal phase diagrams.
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The analog of two seminal quantum optics experiments are considered in a condensed matter setting with single electron sources injecting electronic wave packets on edge states coupled through a quantum point contact. When only one electron is injecte
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