Quantum walks simulating non-commutative geometry in the Landau problem - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue J.Math.Phys. Année : 2021

Quantum walks simulating non-commutative geometry in the Landau problem

Résumé

Non-Commutative Geometry (NCG) is considered in the context of a charged particle moving in a uniform magnetic field. The classical and quantum mechanical treatments are revisited, and a new marker of NCG is introduced. This marker is then used to investigate NCG in magnetic Quantum Walks (QWs). It is proven that these walks exhibit NCG at and near the continuum limit. For the purely discrete regime, two illustrative walks of different complexities are studied in full detail. The most complex walk does exhibit NCG, but the simplest, most degenerate one does not. Thus, NCG can be simulated by QWs, not only in the continuum limit but also in the purely discrete regime.
Fichier principal
Vignette du fichier
5.0030191.pdf (4.17 Mo) Télécharger le fichier
Origine : Publication financée par une institution

Dates et versions

hal-03288769 , version 1 (20-09-2021)

Identifiants

Citer

F. Debbasch. Quantum walks simulating non-commutative geometry in the Landau problem. J.Math.Phys., 2021, 62 (6), pp.062205. ⟨10.1063/5.0030191⟩. ⟨hal-03288769⟩
65 Consultations
23 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More