2012/02/20 by Max Lein, Lein, Max
Materials Science · Mathematics · Physics and Astronomy · #FOS: Physical sciences #Graphene research and applications #Mathematical Physics (math-ph) #Spectral Theory in Mathematical Physics #Surface and Thin Film Phenomena
paper · pdf · doi:10.48550/arxiv.1202.4668
openalex publication_date 2012/02/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Weyl quantization and related semiclassical techniques can be used to study conduction properties of crystalline solids subjected to slowly-varying, external electromagnetic fields. The case where the external magnetic field is constant, is not covered by existing theory as proofs involving usual Weyl calculus break down. This is the regime of the so-called quantum Hall effect where quantization of transverse conductance is observed. To rigorously derive semiclassical equations of motion, one needs to systematically develop a magnetic Weyl calculus which contains a semiclassical parameter. Mathematically, the operators involved in the analysis are magnetic pseudodifferential operators, a topic which by itself is of interest for the mathematics and mathematical physics community alike. Hence, we will devote two additional chapters to further understanding of properties of those operators.