Quantum transport in lattices subjected to external gauge fields
Nathan Goldman
Broschiertes Buch

Quantum transport in lattices subjected to external gauge fields

The quantum Hall effect in optical lattices and quantum graphs

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At low temperature, the transverse transport ofparticles subjected to an external magnetic field is quantized. Thisquantum Hall effect is elegantly described at the single-particle levelin terms of topological invariants called the Chern numbers.In this work, one presents several methods that allowthe numerical and analytical computation of these Chern numbers fora huge variety of physical systems. In particular, one applies these methods to ultracoldatoms trapped in optical lattices and subjected to external Abelianand non-Abelian gaugefields. Then one investigates thespectral properties of q...