title: Fractal energy carpets in non-Hermitian Hofstadter quantum mechanics.
abstract: We study the non-Hermitian Hofstadter dynamics of a quantum particle with biased motion on a square lattice in the background of a magnetic field. We show that in quasimomentum space, the energy spectrum is an overlap of infinitely many inequivalent fractals. The energy levels in each fractal are space-filling curves with Hausdorff dimension 2. The band structure of the spectrum is similar to a fractal spider web in contrast to the Hofstadter butterfly for unbiased motion.
authors.affiliation: CNRS, Laboratoire de Mathématiques et Physique Théorique, UMR 7350, Université de Tours, 37200 Tours, France; Department of Physics and Astronomy, University of Gent, Krijgslaan 281, S9, B-9000 Gent, Belgium; and Soft Matter Physics Laboratory, Far Eastern Federal University, Sukhanova str., 8, Vladivostok 690950, Russia.
authors.forename: Maxim N
authors.initials: MN
authors.lastname: Chernodub
authors.affiliation: CNRS, Laboratoire de Physique Théorique et Modèles Statistiques, UMR 8626, Université Paris-Sud, 91405 Orsay, France.
authors.forename: Stéphane
authors.initials: S
authors.lastname: Ouvry