Cantor spectra of magnetic chain graphs. (16th March 2017)

• Record Type: Journal Article
• Authors: Exner, Pavel; Vašata, Daniel
• Is Part Of: Journal of physics. Volume 50:Number 16(2017)
• Publication Date: 2017-03-16
• Subjects: quantum chain graph -- magnetic field -- almost Mathieu operator -- Cantor spectrum; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/aa6328
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: We demonstrate a one-dimensional magnetic system can exhibit a Cantor-type spectrum using an example of a chain graph with δ coupling at the vertices exposed to a magnetic field perpendicular to the graph plane and varying along the chain. If the field grows linearly with an irrational slope, measured in terms of the flux through the loops of the chain, we demonstrate the character of the spectrum relating it to the almost Mathieu operator.