Characterization of bulk states in one-edge quantum Hall systems
SOCCORSI, Eric
Centre de Physique Théorique - UMR 7332 [CPT]
CPT - E8 Dynamique quantique et analyse spectrale
Centre de Physique Théorique - UMR 7332 [CPT]
CPT - E8 Dynamique quantique et analyse spectrale
SOCCORSI, Eric
Centre de Physique Théorique - UMR 7332 [CPT]
CPT - E8 Dynamique quantique et analyse spectrale
< Leer menos
Centre de Physique Théorique - UMR 7332 [CPT]
CPT - E8 Dynamique quantique et analyse spectrale
Idioma
en
Article de revue
Este ítem está publicado en
Annales Henri Poincaré. 2016, vol. 17, n° 1, p. 37-62
Springer Verlag
Resumen en inglés
We study magnetic quantum Hall systems in a half-plane with Dirichlet boundary conditions along the edge. Much work has been done on the analysis of the currents associated with states whose energy is located between Landau ...Leer más >
We study magnetic quantum Hall systems in a half-plane with Dirichlet boundary conditions along the edge. Much work has been done on the analysis of the currents associated with states whose energy is located between Landau levels. These edge states are localized near the boundary and they carry a non-zero current. In this article, we study the behavior of states with energy close to a Landau level that are referred to as bulk states in the physics literature. The magnetic Schrödinger operator is invariant with respect to translations in the direction of the edge and is a direct integral of operators indexed by a real wave number. We analyse the fiber operators and prove new asymptotics on the band functions and their first derivative as the wave number goes to infinity. We apply these results to prove that the current carried by a bulk state is small compared to the current carried by an edge state. We also prove that the bulk states are exponentially small near the edge.< Leer menos
Palabras clave en inglés
constant magnetic field
Two-dimensional Schrödinger operator
Proyecto ANR
INITIATIVE D'EXCELLENCE AIX MARSEILLE UNIVERSITE - ANR-11-IDEX-0001
ARCHIMEDE / Mathématiques - ANR-11-LABX-0033
ARCHIMEDE / Mathématiques - ANR-11-LABX-0033
Orígen
Importado de HalCentros de investigación