Gap-labelling conjecture with nonzero magnetic field - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Advances in Mathematics Année : 2018

Gap-labelling conjecture with nonzero magnetic field

Varghese Mathai
  • Fonction : Auteur

Résumé

Given a constant magnetic field on Euclidean space ${\mathbb R}^p$ determined by a skew-symmetric $(p\times p)$ matrix $\Theta$, and a ${\mathbb Z}^p$-invariant probability measure $\mu$ on the disorder set $\Sigma$ which is by hypothesis a Cantor set, where the action is assumed to be minimal, the corresponding Integrated Density of States of any self-adjoint operator affiliated to the twisted crossed product algebra $C(\Sigma) \rtimes_\sigma {\mathbb Z}^p$, where $\sigma$ is the multiplier on ${\mathbb Z}^p$ associated to $\Theta$, takes on values on spectral gaps in the magnetic gap-labelling group. The magnetic frequency group is defined as an explicit countable subgroup of $\mathbb R$ involving Pfaffians of $\Theta$ and its sub-matrices. We conjecture that the magnetic gap labelling group is a subgroup of the magnetic frequency group. We give evidence for the validity of our conjecture in 2D, 3D, the Jordan block diagonal case and the periodic case in all dimensions.
Fichier principal
Vignette du fichier
hdl_117227.pdf (669.94 Ko) Télécharger le fichier
Origine : Fichiers éditeurs autorisés sur une archive ouverte

Dates et versions

hal-01827033 , version 1 (18-03-2024)

Identifiants

Citer

Moulay Tahar Benameur, Varghese Mathai. Gap-labelling conjecture with nonzero magnetic field. Advances in Mathematics, 2018, 325, pp.116-64. ⟨10.1016/j.aim.2017.11.030⟩. ⟨hal-01827033⟩
32 Consultations
1 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More